This is my modification of user:Cyp's image:Poly.pov povray macros. I don't know (yet) how to upload a .pov file - wikipedia complains that it is not a known image type. Oh well. It also screws up with html encoding. (too bad!)
Progress
editUpdated 01:37, 5 Nov 2004 (UTC) to include more cut+paste polyhedra and a new optimisation procedure to get the "sporadic" ones -- currently only the Snub_disphenoid.
Updated 00:14, 8 Nov 2004 (UTC)
- Further sporadic Johnson solids (See Talk:Johnson solid) J85, J86, J88, J89
- A rudimentary automatic-framing solution to minimise excess whitespace. This means a whole stack of poorly-framed images will need redoing.
Todo
edit- Modify augment(n,a,b,c) to work with n=4,5 (square, pentagonal pyramid) n=6,8,10 (cupolae)
- Finish sporadics using optimise()
- Finish set of cuboctahedron modifications (very similar to work already done)
- Many not very interesting polyhedra from putting cupolae on various faces of archimedean solids.
//Picture *** Use flashiness=1 !!! ***
//
// +w1024 +h1024 +a0.3 +am2
// +w512 +h512 +a0.3 +am2
//
//Movie *** Use flashiness=0.25 !!! ***
//
// +kc +kff120 +w256 +h256 +a0.3 +am2
// +kc +kff60 +w256 +h256 +a0.3 +am2
//"Fast" preview
// +w128 +h128
#declare notwireframe=1;
#declare withreflection=0;
#declare flashiness=0.25; //Still pictures use 1, animated should probably be about 0.25.
#macro This_shape_will_be_drawn()
//PLATONIC SOLIDS ***********
//tetrahedron() #declare rotation=seed(1889/*1894*/);
//hexahedron() #declare rotation=seed(7122);
//octahedron() #declare rotation=seed(4193);
//dodecahedron() #declare rotation=seed(4412);
//icosahedron() #declare rotation=seed(7719);
//weirdahedron() #declare rotation=seed(7412);
//ARCHIMEDIAN SOLIDS ***********
//cuboctahedron() #declare rotation=seed(1941);
//icosidodecahedron() #declare rotation=seed(2241);
//truncatedtetrahedron(0) #declare rotation=seed(8717);
//truncatedhexahedron(0) #declare rotation=seed(1345);
//truncatedoctahedron() #declare rotation=seed(7235);
//truncateddodecahedron(0) #declare rotation=seed(9374);
//truncatedicosahedron() #declare rotation=seed(1666);
//rhombicuboctahedron() #declare rotation=seed(6124);
//truncatedcuboctahedron() #declare rotation=seed(1156);
//rhombicosidodecahedron() #declare rotation=seed(8266);
//truncatedicosidodecahedron() #declare rotation=seed(1422);
//snubhexahedron(-1) #declare rotation=seed(7152);
//snubhexahedron(1) #declare rotation=seed(1477);
//snubdodecahedron(-1) #declare rotation=seed(5111);
//snubdodecahedron(1) #declare rotation=seed(8154);
//CATALAN SOLIDS ***********
//rhombicdodecahedron() #declare rotation=seed(7154);
//rhombictriacontahedron() #declare rotation=seed(1237);
//triakistetrahedron() #declare rotation=seed(7735);
//triakisoctahedron() #declare rotation=seed(5354);
//tetrakishexahedron() #declare rotation=seed(1788);
//triakisicosahedron() #declare rotation=seed(1044);
//pentakisdodecahedron() #declare rotation=seed(6100);
//deltoidalicositetrahedron() #declare rotation=seed(5643);
//disdyakisdodecahedron() #declare rotation=seed(1440);
//deltoidalhexecontahedron() #declare rotation=seed(1026);
//disdyakistriacontahedron() #declare rotation=seed(1556);
//pentagonalicositetrahedron(-1) #declare rotation=seed(7771);
//pentagonalicositetrahedron(1) #declare rotation=seed(3470);
//pentagonalhexecontahedron(-1) #declare rotation=seed(1046);
//pentagonalhexecontahedron(1) #declare rotation=seed(1096);
//PRISMS, ANTIPRISMS, ETC... ***********
//rprism(5) #declare rotation=seed(6620);
//antiprism(5) #declare rotation=seed(6620);
//bipyramid(5) #declare rotation=seed(6620);
//trapezohedron(17) #declare rotation=seed(6620);
// JOHNSON SOLIDS (AGK)
//square_pyramid() #declare rotation=seed(84); // J1
//pentagonal_pyramid() #declare rotation=seed(11); // J2
//triangular_cupola() #declare rotation=seed(11); // J3
//square_cupola() #declare rotation=seed(19); // J4
//pentagonal_cupola() #declare rotation=seed(19); // J5
//pentagonal_rotunda() #declare rotation=seed(4); // J6
//elongated_pyramid(3) #declare rotation=seed(444);// J7
//elongated_pyramid(4) #declare rotation=seed(444);// J8
//elongated_pyramid(5) #declare rotation=seed(444);// J9
//gyroelongated_square_pyramid() #declare rotation=seed(6621); // J10
//gyroelongated_pentagonal_pyramid() #declare rotation=seed(6621); // J11
//dipyramid(3) #declare rotation=seed(654);// J12
//dipyramid(5) #declare rotation=seed(654);// J13
//elongated_dipyramid(3) #declare rotation=seed(654);// J14
//elongated_dipyramid(4) #declare rotation=seed(654);// J15
//elongated_dipyramid(5) #declare rotation=seed(654);// J16
//gyroelongated_square_dipyramid() #declare rotation=seed(6621); // J17
//elongated_triangular_cupola() #declare rotation=seed(112358); //J18
//elongated_square_cupola() #declare rotation=seed(333); // J19
//elongated_pentagonal_cupola() #declare rotation=seed(333); //J20
//elongated_pentagonal_rotunda() #declare rotation=seed(4); // J21
//gyroelongated_triangular_cupola() #declare rotation=seed(112358); //J22
//gyroelongated_square_cupola() #declare rotation=seed(333); // J23
//gyroelongated_pentagonal_cupola() #declare rotation=seed(333); //J24
//gyroelongated_pentagonal_rotunda() #declare rotation=seed(4); // J25
//gyrobifastigium() #declare rotation=seed(112358); // J26
//triangular_orthobicupola() #declare rotation=seed(112358); //J27
//square_orthobicupola() #declare rotation=seed(333); // J28
//square_gyrobicupola() #declare rotation=seed(333); // J29
//pentagonal_orthobicupola() #declare rotation=seed(333); //J30
//pentagonal_gyrobicupola() #declare rotation=seed(333); //J31
//pentagonal_orthocupolarotunda() #declare rotation=seed(4); //J32
//pentagonal_gyrocupolarotunda() #declare rotation=seed(4); //J33
//pentagonal_orthobirotunda() #declare rotation=seed(4); // J34
//elongated_triangular_orthobicupola() #declare rotation=seed(112358); //J35
//elongated_triangular_gyrobicupola() #declare rotation=seed(112358); //J36
//elongated_square_gyrobicupola() #declare rotation=seed(333); // J37
//elongated_pentagonal_orthobicupola() #declare rotation=seed(333); //J38
//elongated_pentagonal_gyrobicupola() #declare rotation=seed(333); //J39
//icosidodecahedron_mod(40) #declare rotation=seed(4); //J40: elongated_pentagonal_orthocupolarotunda
//icosidodecahedron_mod(41) #declare rotation=seed(4); //J41: elongated_pentagonal_gyrocupolarotunda
//elongated_pentagonal_orthobirotunda() #declare rotation=seed(4); // J42
//elongated_pentagonal_gyrobirotunda() #declare rotation=seed(4); // J43
//gyroelongated_triangular_bicupola() #declare rotation=seed(112358); //J44
//gyroelongated_square_bicupola() #declare rotation=seed(333); // J45
//gyroelongated_pentagonal_bicupola() #declare rotation=seed(333); //J46
//icosidodecahedron_mod(47) #declare rotation=seed(4); //J47: gyroelongated_pentagonal_cupolarotunda
//gyroelongated_pentagonal_birotunda() #declare rotation=seed(4); // J48
//augmented_triangular_prism() #declare rotation=seed(88);// J49
//biaugmented_triangular_prism() #declare rotation=seed(88);// J50
//triaugmented_triangular_prism() #declare rotation=seed(88);// J51
//augmented_pentagonal_prism() #declare rotation=seed(5555);// J52
//biaugmented_pentagonal_prism() #declare rotation=seed(5555);// J53
//augmented_hexagonal_prism() #declare rotation=seed(5555);// J54
//parabiaugmented_hexagonal_prism() #declare rotation=seed(5555);// J55
//metabiaugmented_hexagonal_prism() #declare rotation=seed(5555);// J56
//triaugmented_hexagonal_prism() #declare rotation=seed(5555);// J56
//augmented_dodecahedron() #declare rotation=seed(4412); // J58
//parabiaugmented_dodecahedron() #declare rotation=seed(4412); // J59
////metabiaugmented_dodecahedron() #declare rotation=seed(4412); // J60
//triaugmented_dodecahedron() #declare rotation=seed(4412); // J61
//metabidiminished_icosahedron() #declare rotation=seed(6621); // J62
//tridiminished_icosahedron() #declare rotation=seed(6621); // J63
//augmented_tridiminished_icosahedron() #declare rotation=seed(6621); // J64
//truncatedtetrahedron(1) #declare rotation=seed(13); // J65 augmented_truncated_tetrahedron.png
//truncatedhexahedron(1) #declare rotation=seed(1345); // J66 augmented_truncated_cube.png
//truncatedhexahedron(2) #declare rotation=seed(1345); // J67 biaugmented_truncated_cube.png
//truncateddodecahedron(1) #declare rotation=seed(19); // J68 augmented_truncated_dodecahedron.png
//truncateddodecahedron(-2) #declare rotation=seed(19); // J69 parabiaugmented_truncated_dodecahedron.png
//truncateddodecahedron(2) #declare rotation=seed(19); // J70 metabiaugmented_truncated_dodecahedron.png
truncateddodecahedron(3) #declare rotation=seed(19); // J71 triaugmented_truncated_dodecahedron.png
//mogrified_rhombicosidodecahedron("G...") #declare rotation=seed(19); // J72 gyrate_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("G..G") #declare rotation=seed(19); // J73 parabigyrate_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("GG..") #declare rotation=seed(19); // J74 metabigyrate_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("GGG.") #declare rotation=seed(19); // J75 trigyrate_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("D...") #declare rotation=seed(19); // J76 diminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("D..G") #declare rotation=seed(19); // J77 paragyrate_diminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("DG..") #declare rotation=seed(19); // J78 metagyrate_diminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("GDG.") #declare rotation=seed(19); // J79 bigyrate_diminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("D..D") #declare rotation=seed(19); // J80 parabidiminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("DD..") #declare rotation=seed(19); // J81 metabidiminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("GDD.") #declare rotation=seed(19); // J82 gyrate_bidiminished_rhombicosidodecahedron.png
//mogrified_rhombicosidodecahedron("DDD.") #declare rotation=seed(19); // J83 tridiminished_rhombicosidodecahedron.png
//gyrate_rhombicosidodecahedron() #declare rotation=seed(19); // J72
//trigyrate_rhombicosidodecahedron() #declare rotation=seed(19); //J75
//diminished_rhombicosidodecahedron() #declare rotation=seed(19); // J76
//parabidiminished_rhombicosidodecahedron() #declare rotation=seed(19); //J80
//metabidiminished_rhombicosidodecahedron() #declare rotation=seed(19); //J81
//tridiminished_rhombicosidodecahedron() #declare rotation=seed(19); // J83
//snub_disphenoid() #declare rotation=seed(142); // J84
//snub_square_antiprism() #declare rotation=seed(418); // J85
//sphenocorona() #declare rotation=seed(11); // J86
//augmented_sphenocorona() #declare rotation=seed(11); // J87
//sphenomegacorona() #declare rotation=seed(11); // J88
//hebesphenomegacorona() #declare rotation=seed(11); // J89
//disphenocingulum() #declare rotation=seed(11); // J90
//bilunabirotunda() #declare rotation=seed(10); // J91
//triangular_hebesphenorotunda() #declare rotation=seed(855); // J92
#end
#declare tau=(1+sqrt(5))/2;
#declare sq2=sqrt(2);
#declare sq297=sqrt(297);
#declare xi=(pow(sq297+17,1/3)-pow(sq297-17,1/3)-1)/3;
#declare sqweird=sqrt(tau-5/27);
#declare ouch=pow((tau+sqweird)/2,1/3)+pow((tau-sqweird)/2,1/3);
#declare alfa=ouch-1/ouch;
#declare veta=(ouch+tau+1/ouch)*tau;
#macro tetrahedron()
addpointsevensgn(<1,1,1>)
autoface()
#end
#macro hexahedron()
addpointssgn(<1,1,1>,<1,1,1>)
autoface()
#end
#macro octahedron()
addevenpermssgn(<1,0,0>,<1,0,0>)
autoface()
#end
#macro dodecahedron()
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
autoface()
#end
#macro icosahedron()
addevenpermssgn(<0,1,tau>,<0,1,1>)
autoface()
#end
#macro weirdahedron()
addpermssgn(<1,2,3>,<1,1,1>)
autoface()
#end
#macro cuboctahedron()
addevenpermssgn(<0,1,1>,<0,1,1>)
autoface()
#end
#macro icosidodecahedron()
addevenpermssgn(<0,0,2*tau>,<0,0,1>)
addevenpermssgn(<1,tau,1+tau>,<1,1,1>)
autoface()
#end
#macro truncatedtetrahedron(augmentation)
addevenpermsevensgn(<1,1,3>)
#if (augmentation)
// augment(6,points[3],points[0],points[1])
augment(6,points[0],points[1],points[4])
#end
autoface()
#end
#macro truncatedhexahedron(augmentation)
addevenpermssgn(<sq2-1,1,1>,<1,1,1>)
#switch (augmentation)
#case(2) augment(8,points[7],points[23],points[22])
#case(1) augment(8,points[16],points[0],points[1])
#end
autoface()
#end
#macro truncatedoctahedron()
addpermssgn(<0,1,2>,<0,1,1>)
autoface()
#end
#macro truncateddodecahedron(augmentation)
addevenpermssgn(<0,1/tau,2+tau>,<0,1,1>)
addevenpermssgn(<1/tau,tau,2*tau>,<1,1,1>)
addevenpermssgn(<tau,2,1+tau>,<1,1,1>)
#if (augmentation)
augment(10,points[50],points[58],points[34]) // towards (tau,-1,0) -- common to all
#switch (augmentation)
#case(3) augment(10,points[54],points[38],points[14]) // towards (-1,0,tau) -- on tri
#case(2) augment(10,points[40],points[48],points[24]) // towards (0,phi,-1) -- on metadi and tri
#break
#case(-2) augment(10,points[32],points[10],points[9]) // towards (-tau,1,0) -- on paradi
#end
#end
autoface()
#end
#macro truncatedicosahedron()
addevenpermssgn(<0,1,3*tau>,<0,1,1>)
addevenpermssgn(<2,1+2*tau,tau>,<1,1,1>)
addevenpermssgn(<1,2+tau,2*tau>,<1,1,1>)
autoface()
#end
#macro rhombicuboctahedron()
addevenpermssgn(<1+sq2,1,1>,<1,1,1>)
autoface()
#end
#macro truncatedcuboctahedron()
addpermssgn(<1,1+sq2,1+sq2*2>,<1,1,1>)
autoface()
#end
#macro rhombicosidodecahedron()
addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
autoface()
#end
#macro truncatedicosidodecahedron()
addevenpermssgn(<1/tau,1/tau,3+tau>,<1,1,1>)
addevenpermssgn(<2/tau,tau,1+2*tau>,<1,1,1>)
addevenpermssgn(<1/tau,1+tau,3*tau-1>,<1,1,1>)
addevenpermssgn(<2*tau-1,2,2+tau>,<1,1,1>)
addevenpermssgn(<tau,3,2*tau>,<1,1,1>)
autoface()
#end
#macro snubhexahedron(s)
addpermsaltsgn(<1,1/xi,xi>*s)
autoface()
#end
#macro snubdodecahedron(s)
addevenpermsevensgn(<2*alfa,2,2*veta>*s)
addevenpermsevensgn(<alfa+veta/tau+tau,-alfa*tau+veta+1/tau,alfa/tau+veta*tau-1>*s)
addevenpermsevensgn(<-alfa/tau+veta*tau+1,-alfa+veta/tau-tau,alfa*tau+veta-1/tau>*s)
addevenpermsevensgn(<-alfa/tau+veta*tau-1,alfa-veta/tau-tau,alfa*tau+veta+1/tau>*s)
addevenpermsevensgn(<alfa+veta/tau-tau,alfa*tau-veta+1/tau,alfa/tau+veta*tau+1>*s)
autoface()
#end
#macro rhombicdodecahedron()
cuboctahedron() dual()
#end
#macro rhombictriacontahedron()
icosidodecahedron() dual()
#end
#macro triakistetrahedron()
truncatedtetrahedron(0) dual()
#end
#macro triakisoctahedron()
truncatedhexahedron(0) dual()
#end
#macro tetrakishexahedron()
truncatedoctahedron() dual()
#end
#macro triakisicosahedron()
truncateddodecahedron(0) dual()
#end
#macro pentakisdodecahedron()
truncatedicosahedron() dual()
#end
#macro deltoidalicositetrahedron()
rhombicuboctahedron() dual()
#end
#macro disdyakisdodecahedron()
truncatedcuboctahedron() dual()
#end
#macro deltoidalhexecontahedron()
rhombicosidodecahedron() dual()
#end
#macro disdyakistriacontahedron()
truncatedicosidodecahedron() dual()
#end
#macro pentagonalicositetrahedron(s)
snubhexahedron(s) dual()
#end
#macro pentagonalhexecontahedron(s)
snubdodecahedron(s) dual()
#end
//>>>>>>>>>>>>>>>>> changed AGK [20041101]
#macro polygon_vtx(n)
#local i=0;
#while (i<n-.5)
addpoint(<cos(i*2*pi/n),sin(i*2*pi/n),0>)
#local i=i+1;
#end
#end
#macro rprism_vtx(n)
#local a=sqrt((1-cos(2*pi/n))/2);
#local b=0; #while(b<n-.5)
addpointssgn(<sin(2*pi*b/n),cos(2*pi*b/n),a>,<0,0,1>)
#local b=b+1; #end
#end
#macro antiprism_vtx(n)
#local a=sqrt((cos(pi/n)-cos(2*pi/n))/2);
#local b=0; #while(b<2*n-.5)
addpoint(<sin(pi*b/n),cos(pi*b/n),a>)
#local a=-a; #local b=b+1; #end
#end
#macro rprism(n)
rprism_vtx(n) autoface()
#end
#macro antiprism(n)
antiprism_vtx(n)
autoface()
#end
//<<<<<<<<<<<<<<<<< changed AGK [20041101]
#macro bipyramid(n)
rprism(n) dual()
#end
#macro trapezohedron(n)
antiprism(n) dual()
#end
//>>>>>>>>>>>>>>>>> added AGK [20041101]
#macro augment(n,va,vb,vc) // on an n-face with 3 adjacent vtxs, add a pyramid or a cupola
#local veci=va-vb; #local vecj=vc-vb; #local veck=vlength(vc-vb)*vnormalize(vcross(vc-vb,va-vb));
#switch(n)
#case (3) addpoint( (va+vb+vc)/3 + sqrt(2/3)*veck ) #break
#case (4) addpoint( (va+vc)/2 + sqrt(1/2)*veck ) #break
#case (5) addpoint( vb+(2+tau)/5*(veci+vecj) + sqrt((3-tau)/5)*veck ) #break
#case (6)
addpoint( vb+1/3*veci + 2/3*vecj + sqrt(2/3)*veck )
addpoint( vb+4/3*veci + 2/3*vecj + sqrt(2/3)*veck )
addpoint( vb+4/3*veci + 5/3*vecj + sqrt(2/3)*veck )
#break
#case (8)
addpoint( vb + sqrt(1/2)*veci + vecj + sqrt(1/2)*veck )
addpoint( vb + (1+sqrt(1/2))*veci + vecj + sqrt(1/2)*veck )
addpoint( vb + (1+sqrt(1/2))*veci + (1+sq2)*vecj + sqrt(1/2)*veck )
addpoint( vb + (2+sqrt(1/2))*veci + (1+sq2)*vecj + sqrt(1/2)*veck )
#break
#case (10)
addpoint( vb+(0.2+0.6*tau)*veci + (0.8+0.4*tau)*vecj + sqrt((3-tau)/5)*veck )
addpoint( vb+(1.2+0.6*tau)*veci + (0.8+0.4*tau)*vecj + sqrt((3-tau)/5)*veck )
addpoint( vb+(1.2+1.6*tau)*veci + (0.8+1.4*tau)*vecj + sqrt((3-tau)/5)*veck )
addpoint( vb+(1.2+1.6*tau)*veci + (1.8+1.4*tau)*vecj + sqrt((3-tau)/5)*veck )
addpoint( vb+(1.2+0.6*tau)*veci + (0.8+1.4*tau)*vecj + sqrt((3-tau)/5)*veck )
#break
#end
#end
#macro rotateabout(raxis,rangle,va) // raxis must be a unit vector
(vdot(raxis,va)*raxis
+ cos(rangle)*(va-vdot(raxis,va)*raxis)
+ sin(rangle)*(vcross(raxis,va)))
#end
#macro rotate_vtxs(raxis,rangle,thresh) // all points in the halfspace v.raxis <= tresh
#local i=0;
#while (i<npoints-.5)
#if (vdot(points[i],raxis) < thresh+0.01)
#declare points[i]=rotateabout(raxis,pi*rangle/180,points[i]);
#end // if
#local i=i+1;
#end //while
#end
#macro drop_vtx(n)
#declare npoints=npoints-1;
#if(n<npoints)
#declare points[n]=points[npoints];
#end
#end
#macro drop_halfspace(normalvector,thresh) // all points in the halfspace v.raxis < tresh
#local i=0;
#while (i<npoints-.5)
#if (vdot(points[i],normalvector)<thresh-0.01)
#debug concat("Drop vtx ",str(i,0,0)," of ",str(npoints,0,0)," <",str(points[i].x,0,3),",",str(points[i].y,0,3),",",str(points[i].z,0,3),"> (",str(vdot(points[i],normalvector),0,7),")\n")
drop_vtx(i)
#else
#debug concat("Keep vtx ",str(i,0,0)," of ",str(npoints,0,0)," <",str(points[i].x,0,3),",",str(points[i].y,0,3),",",str(points[i].z,0,3),"> (",str(vdot(points[i],normalvector),0,7),")\n")
#local i=i+1;
#end
#end
#end
#macro autobalance() // moves the centre of gravity (cog) of the vertices to the origin
#local cog=<0,0,0>;
#local i=0;
#while (i<npoints-.5)
#local cog=cog+points[i];
#local i=i+1;
#end
#local cog=cog/npoints;
#local i=0;
#while (i<npoints-.5)
#declare points[i]=points[i] - cog;
#local i=i+1;
#end
#end
#macro showvtxs()
#local i=0;
#while (i<npoints-.5)
#debug concat("Vtx ",str(i,0,0)," of ",str(npoints,0,0),"= <",str(points[i].x,0,7),",",str(points[i].y,0,7),",",str(points[i].z,0,7),">\n")
#local i=i+1;
#end
#end
#macro drawit()
#local i=0;
#while (i<npoints)
sphere { points[i], .05 dorot()
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 } }
#local j=0;
#while (j<npoints)
#ifdef(edgelen[i][j])
#local dist=vlength(points[i]-points[j]);
cylinder { points[i],points[j], .02 dorot()
pigment {
#switch (dist-edgelen[i][j])
#range (-999,-0.1) colour <1,0,0> #break
#range (0.1,999) colour <0,0,1> #break
#else
colour <.3,.3,.3>
#end
#debug concat("Edge ",str(i,0,0)," & ",str(j,0,0)," has length ",str(dist,5,5)," want length ",str(edgelen[i][j],5,5),"\n")
}
finish { ambient 0 diffuse 1 phong 1 } }
#end
#local j=j+1;
#end
#local i=i+1;
#end
#end
//--------------- macros to find "sporadic" Johnson solids via iterative optimisation kludge
#declare el=1;
#declare edgelen=array[120][120];
#declare forces=array[120];
#macro addedge(a,b,len)
#declare edgelen[a][b]=len;
#declare edgelen[b][a]=len;
#end
#macro make_triangle(a,b,c)
addedge(a,b,el) addedge(a,c,el) addedge(b,c,el)
#end
#macro make_square(a,b,c,d)
addedge(a,b,el) addedge(b,c,el) addedge(c,d,el) addedge(d,a,el) addedge(a,c,sq2*el) addedge(b,d,sq2*el)
#end
#macro make_lune(a,b,c,d,e,f) // a and d are points of lune
make_triangle(a,b,f) make_square(b,c,e,f) make_triangle(c,d,e)
#end
#macro optimise(gen_threshold,force_threshold)
#local gen=0; #local maxforce=force_threshold+1;
#while ((gen<gen_threshold) & (maxforce>force_threshold))
#debug concat("Gen ",str(gen,0,0)," ")
// showvtxs()
#local maxforce=-999;
#local i=0;
#while (i<npoints)
#declare forces[i]=<0,0,0>;
#local j=0;
#while (j<npoints)
#ifdef(edgelen[i][j])
#local dist=vlength(points[i]-points[j]);
#declare forces[i] = forces[i]+ (dist-edgelen[i][j])*(points[j]-points[i]);
// #debug concat("Edge ",str(i,0,0)," & ",str(j,0,0)," has length ",str(dist,5,5)," want length ",str(edgelen[i][j],5,5),"\n")
#end
#local j=j+1;
#end
#if (maxforce<vlength(forces[i])) #local maxforce=vlength(forces[i]); #end
#local i=i+1;
#end
#debug concat("maxforce=",str(maxforce,9,9),"\n")
#local i=0;
#while (i<npoints)
#declare points[i]=points[i]+.1*forces[i];
#local i=i+1;
#end
#local gen=gen+1;
#end
#end
// Johnson solids
// J1 = square_pyramid (octahedron with vtx dropped)
#macro square_pyramid()
addevenpermssgn(<1,0,0>,<1,0,0>) drop_vtx(99)
autobalance() autoface()
#end
// J2 = pentagonal_pyramid (six vtxs of an icosahedron)
#macro pentagonal_pyramid()
addevenpermssgn(<0,1,tau>,<0,1,1>) drop_halfspace(points[0],0)
autobalance() autoface()
#end
// ----------------- cuboctahedron modifications J - 3, 18, 22, 27, 35, 36, 44
// J3 = triangular_cupola (9 vtxs of a cuboctahedron)
#macro triangular_cupola()
polygon_vtx(6)
augment(6,points[0],points[1],points[2])
autobalance() autoface()
#end
#macro triangular_gyrobicupola() //actually a cuboctahedron
polygon_vtx(6)
augment(6,points[0],points[1],points[2])
augment(6,points[2],points[1],points[0])
autobalance() autoface()
#end
#macro elongated_triangular_cupola() //J18
rprism_vtx(6)
augment(6,points[1],points[3],points[5])
autobalance() autoface()
#end
#macro gyroelongated_triangular_cupola() //J22
antiprism_vtx(6)
augment(6,points[1],points[3],points[5])
autobalance() autoface()
#end
#macro triangular_orthobicupola() //J27
polygon_vtx(6)
augment(6,points[0],points[1],points[2])
augment(6,points[3],points[2],points[1])
autobalance() autoface()
#end
#macro elongated_triangular_orthobicupola() //J35
rprism_vtx(6)
augment(6,points[1],points[3],points[5])
augment(6,points[6],points[4],points[2])
autobalance() autoface()
#end
#macro elongated_triangular_gyrobicupola() //J36
rprism_vtx(6)
augment(6,points[1],points[3],points[5])
augment(6,points[4],points[2],points[0])
autobalance() autoface()
#end
#macro gyroelongated_triangular_bicupola() //J44
antiprism_vtx(6)
augment(6,points[1],points[3],points[5])
augment(6,points[4],points[2],points[0])
autobalance() autoface()
#end
// two triangular prisms
#macro gyrobifastigium() // J26
addpointssgn(<1,1,0>,<1,1,0>)
addpointssgn(<1,0,sqrt(3)>,<1,0,0>)
addpointssgn(<0,1,-sqrt(3)>,<0,1,0>)
autobalance() autoface()
#end
//---------------- miscellaneous cut and pasting
#macro elongated_pyramid(n) // J7-9 (for n=3,4,5)
rprism_vtx(n)
augment(n,points[4],points[2],points[0])
autobalance() autoface()
#end
#macro dipyramid(n) // J12 (n=3) and J13 (n=5)
polygon_vtx(n)
augment(n,points[0],points[1],points[2])
augment(n,points[2],points[1],points[0])
autobalance() autoface()
#end
#macro elongated_dipyramid(n) // J14-16 (for n=3,4,5)
rprism_vtx(n)
augment(n,points[4],points[2],points[0])
augment(n,points[1],points[3],points[5])
autobalance() autoface()
#end
#macro elongated_triangular_dipyramid() elongated_dipyramid(3) #end // J7
#macro elongated_square_dipyramid() elongated_dipyramid(3) #end // J8
#macro elongated_pentagonal_dipyramid() elongated_dipyramid(3) #end // J9
// ----------------- rhombicuboctahedron modifications J - 4, 19, 23, 28, 29, 37, 45
#macro rhombicuboctahedron_mod(j_number)
addevenpermssgn(<1+sq2,1,1>,<1,1,1>)
#local raxis=x;
#local edgelen=2;
#local oct_radius=sqrt(2*sq2+4);
// drop hemisphere for 6, 21, 25 (have single rotunda)
#if(j_number=4) drop_halfspace(raxis,1) #end
#if(j_number<=23) drop_halfspace(raxis,-1) #end
// stretch and twist
#local stretch=0; #local twist=0;
#switch(j_number)
#case(29)
#local twist=45;
#case(28)
#local stretch=-edgelen;
#break
#case(37)
#local twist=45;
#break
#case(23) #case(45)
#local twist=22.5;
#local stretch=oct_radius*2*sqrt((cos(pi/8)-cos(2*pi/8))/2)-edgelen; // borrowed from antiprism_vtx
#end //switch
#if (stretch!=0) // lower northern hemisphere
#local i=0;
#while (i<npoints-.5)
#if ((stretch = -2) & ( vdot(points[i],raxis)=1))
drop_vtx(i)
#else
#if (vdot(points[i],raxis)>0)
#declare points[i]=points[i] + stretch*raxis;
#end // if
#local i=i+1;
#end //if
#end //while
#end //if
#if (twist!=0) // rotate southern hemisphere (incl equator)
rotate_vtxs(raxis,twist,-1)
#end
autobalance()
#end
// Now the named macros of these modified rhombicuboctahedron
#macro square_cupola() rhombicuboctahedron_mod(4) autoface() #end // J4
#macro elongated_square_cupola() rhombicuboctahedron_mod(19) autoface() #end // J19
#macro gyroelongated_square_cupola() rhombicuboctahedron_mod(23) autoface() #end // J23
#macro square_orthobicupola() rhombicuboctahedron_mod(28) autoface() #end // J28
#macro square_gyrobicupola() rhombicuboctahedron_mod(29) autoface() #end // J29
#macro elongated_square_gyrobicupola() rhombicuboctahedron_mod(37) autoface() #end // J37
#macro gyroelongated_square_bicupola() rhombicuboctahedron_mod(45) autoface() #end // J45
#macro elongated_square_cupola_alt() // J19
rprism_vtx(8)
augment(8,points[4],points[2],points[0])
autoface() #end
// J10. (cap a square antiprism)
#macro gyroelongated_square_pyramid()
antiprism_vtx(4)
#local va=points[1];
addpoint(<0,0,-(abs(va.z)+1)>)
autoface()
#end
// J17. (bicap a square antiprism)
#macro gyroelongated_square_dipyramid()
antiprism_vtx(4)
#local va=points[1];
addpoint(<0,0,abs(va.z)+1>)
addpoint(<0,0,-(abs(va.z)+1)>)
autoface()
#end
// ----------------- icosahedron modifications
// J11. (drop a vertex from an icosahedron)
#macro gyroelongated_pentagonal_pyramid()
addevenpermssgn(<0,1,tau>,<0,1,1>)
drop_vtx(99)
autoface()
#end
// J62. (drop 2 vertices from an icosahedron)
#macro metabidiminished_icosahedron()
addevenpermssgn(<0,1,tau>,<0,1,1>)
drop_vtx(99)
drop_vtx(6)
autoface()
#end
// J63. (drop 3 vertices from an icosahedron)
#macro tridiminished_icosahedron()
addevenpermssgn(<0,1,tau>,<0,1,1>)
drop_vtx(99)
drop_vtx(6)
drop_vtx(0) // 5 OK too
autoface()
#end
// J64. (drop 3 vertices from an icosahedron, add a tetrahedron)
#macro augmented_tridiminished_icosahedron()
addevenpermssgn(<0,1,tau>,<0,1,1>)
drop_vtx(99)
drop_vtx(6)
drop_vtx(0)
augment(3,points[1],points[7],points[8])
autoface()
#end
// -------------------- dodecahedron modifications: J58-61
#macro augmented_dodecahedron() //J58
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
augment(5,points[4],points[13],points[12])
showvtxs()
autobalance() autoface()
#end
#macro parabiaugmented_dodecahedron() //J59
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
augment(5,points[4],points[13],points[12])
#local a=points[npoints-1];
addpoint(-a)
showvtxs()
autobalance() autoface()
#end
#macro metabiaugmented_dodecahedron() //J60
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
augment(5,points[4],points[13],points[12])
#local a=points[npoints-1];
addpoint(<a.y,a.z,a.x>)
showvtxs()
autobalance() autoface()
#end
#macro triaugmented_dodecahedron() //J61
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
augment(5,points[4],points[13],points[12])
#local a=points[npoints-1]; drop_vtx(999)
addevenperms(a)
showvtxs()
autobalance() autoface()
#end
// ----------------- icosidodecahedron modifications
// Modified icosidodecahedron, for J- 6, 21, 25, 34, 42, 43, 48; J32,33,40,41,47
#macro icosidodecahedron_mod(j_number)
addevenpermssgn(<0,0,2*tau>,<0,0,1>)
addevenpermssgn(<1,tau,1+tau>,<1,1,1>)
#local raxis=vnormalize(<tau,1,0>);
#local edgelen=vlength(<0,0,2*tau>-<1,tau,1+tau>);
#local id_radius=2*tau;
// drop hemisphere for 6, 21, 25 (have single rotunda)
#if((j_number<=33) | (j_number=40) | (j_number=41) | (j_number=47))
drop_halfspace(raxis,0)
#if (j_number>=32) // form a cupolarotunda
augment(10,points[0],points[7],points[15])
#end
#end
// stretch and twist
#local stretch=0; #local twist=0;
#switch(j_number)
#case(42) #case(40)
#local stretch=edgelen;
#case(34) #case(33)
#local twist=36;
#break
#case(21) #case(43) #case(41)
#local stretch=edgelen;
#break
#case(25) #case(48) #case(47)
#local twist=18;
#local stretch=id_radius*2*sqrt((cos(pi/10)-cos(2*pi/10))/2); // borrowed from antiprism_vtx
#end //switch
#if (stretch>0) // raise northern hemisphere, duplicate equator
#local i=0; #local np=npoints;
#while (i<np-.5)
#switch (vdot(points[i],raxis))
#range(-0.01,0.01)
// #debug concat("Dupl. vtx ",str(i,0,0)," of ",str(npoints,0,0)," <",str(points[i].x,0,3),",",str(points[i].y,0,3),",",str(points[i].z,0,3),">\n")
addpoint(points[i] + stretch*raxis)
#break
#range(0.01,999)
// #debug concat("Raise vtx ",str(i,0,0)," of ",str(npoints,0,0)," <",str(points[i].x,0,3),",",str(points[i].y,0,3),",",str(points[i].z,0,3),">\n")
#declare points[i]=points[i] + stretch*raxis;
#break
#end // switch
#local i=i+1;
#end //while
#end //if
#if (twist!=0) // rotate southern hemisphere (incl equator)
rotate_vtxs(raxis,twist,0)
#end
showvtxs()
autobalance() autoface()
#end
#macro pentagonal_rotunda() icosidodecahedron_mod(6) #end // J6. Half an icosidodecahedron
#macro elongated_pentagonal_rotunda() icosidodecahedron_mod(21) #end // J21. Half an icosidodecahedron on a prism
#macro gyroelongated_pentagonal_rotunda() icosidodecahedron_mod(25) #end // J25. Half an icosidodecahedron on an antiprism
#macro pentagonal_orthobirotunda() icosidodecahedron_mod(34) #end // J34. Twisted icosidodecahedron
#macro elongated_pentagonal_gyrobirotunda() icosidodecahedron_mod(43) #end // J43. Elongated icosidodecahedron
#macro elongated_pentagonal_orthobirotunda() icosidodecahedron_mod(42) #end // J42. Elongated twisted icosidodecahedron
#macro gyroelongated_pentagonal_birotunda() icosidodecahedron_mod(48) #end // J48. Elongated semitwisted icosidodecahedron
#macro pentagonal_orthocupolarotunda() icosidodecahedron_mod(32) #end //J32
#macro pentagonal_gyrocupolarotunda() icosidodecahedron_mod(33) #end //J32
//---------------------- pentagonal cupolae, bicupolae
#macro elongated_pentagonal_cupola() //J20
rprism_vtx(10)
augment(10,points[4],points[2],points[0])
autobalance() autoface()
#end
#macro gyroelongated_pentagonal_cupola() //J24
antiprism_vtx(10)
augment(10,points[4],points[2],points[0])
autobalance() autoface()
#end
#macro pentagonal_orthobicupola() //J30
polygon_vtx(10)
augment(10,points[0],points[1],points[2])
augment(10,points[3],points[2],points[1])
autobalance() autoface()
#end
#macro pentagonal_gyrobicupola() //J31
polygon_vtx(10)
augment(10,points[0],points[1],points[2])
augment(10,points[2],points[1],points[0])
autobalance() autoface()
#end
#macro elongated_pentagonal_orthobicupola() //J38
rprism_vtx(10)
augment(10,points[4],points[2],points[0])
augment(10,points[3],points[5],points[7])
autobalance() autoface()
#end
#macro elongated_pentagonal_gyrobicupola() //J39
rprism_vtx(10)
augment(10,points[4],points[2],points[0])
augment(10,points[1],points[3],points[5])
showvtxs()
autobalance() autoface()
#end
#macro gyroelongated_pentagonal_bicupola() //J46
antiprism_vtx(10)
augment(10,points[4],points[2],points[0])
augment(10,points[1],points[3],points[5])
autobalance() autoface()
#end
// -------------------- side-capped prisms : J49-57
#macro augmented_prisms(n,facelist) // n=prism base, facelist=string with faces to cap
rprism_vtx(n)
#local i=1;
#while(i<=strlen(facelist))
#local facenum=mod(val(substr(facelist,i,1)),n); // convert ith char given to a number 0..(n-1)
augment(4,points[2*facenum+1],points[2*facenum],points[mod(2*facenum+2,2*n)])
// #debug concat("Augment face ",str(facenum,0,0)," of ",str(n,0,0), " <",str(points[npoints-1].x,0,3),",",str(points[npoints-1].y,0,3),",",str(points[npoints-1].z,0,3),"> \n")
#local i=i+1;
#end
autobalance() autoface()
#end
#macro augmented_triangular_prism() augmented_prisms(3,"0") #end // J49
#macro biaugmented_triangular_prism() augmented_prisms(3,"01") #end // J50
#macro triaugmented_triangular_prism() augmented_prisms(3,"012") #end // J51
#macro augmented_pentagonal_prism() augmented_prisms(5,"0") #end // J52
#macro biaugmented_pentagonal_prism() augmented_prisms(5,"02") #end // J53
#macro augmented_hexagonal_prism() augmented_prisms(6,"0") #end // J54
#macro parabiaugmented_hexagonal_prism() augmented_prisms(6,"03") #end // J55
#macro metabiaugmented_hexagonal_prism() augmented_prisms(6,"02") #end // J56
#macro triaugmented_hexagonal_prism() augmented_prisms(6,"024") #end // J57
// ----------------- rhombicosidodecahedron modifications
#macro pentagonal_cupola() //J5
addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
#local raxis=vnormalize(<tau,-1,0>);
drop_halfspace(raxis,3.077)
autobalance() autoface()
#end
#macro mogrified_rhombicosidodecahedron(mods) //J72-J83
// mods is a 4-character string of D (drop), G (gyrate) and other (leave alone)
addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
#local raxis=array[5];
#local raxis[1]=vnormalize(<tau,-1,0>);
#local raxis[2]=vnormalize(<-1,0,tau>);
#local raxis[3]=vnormalize(<-1,0,-tau>);
#local raxis[4]=-raxis[1];
#local i=1;
#while(i<=min(4,strlen(mods)))
#local modchar=substr(mods,i,1);
#if (strcmp(modchar,"D")=0) drop_halfspace(-raxis[i],-3.077) #end
#if (strcmp(modchar,"G")=0) rotate_vtxs(-raxis[i],36,-3.077) #end
#local i=i+1;
#end
autobalance() autoface()
#end
// #macro diminished_rhombicosidodecahedron() //J76
// addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
// addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
// addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
// #local raxis=vnormalize(<tau,-1,0>);
// drop_halfspace(-raxis,-3.077)
// autobalance() autoface()
// #end
// #macro tridiminished_rhombicosidodecahedron() //J83
// addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
// addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
// addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
// #local raxis=vnormalize(<tau,-1,0>);
// drop_halfspace(-raxis,-3.077)
// #local raxis=vnormalize(<-1,0,-tau>);
// drop_halfspace(-raxis,-3.077)
// #local raxis=vnormalize(<-1,0,tau>);
// drop_halfspace(-raxis,-3.077)
// autobalance() autoface()
// #end
// #macro metabidiminished_rhombicosidodecahedron() //J81
// addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
// addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
// addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
// #local raxis=vnormalize(<tau,-1,0>);
// drop_halfspace(-raxis,-3.077)
// #local raxis=vnormalize(<-1,0,tau>);
// drop_halfspace(-raxis,-3.077)
// autobalance() autoface()
// #end
// #macro parabidiminished_rhombicosidodecahedron() //J80
// addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
// addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
// addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
// #local raxis=vnormalize(<tau,-1,0>);
// drop_halfspace(-raxis,-3.077)
// drop_halfspace( raxis,-3.077)
// autobalance() autoface()
// #end
//
// #macro gyrate_rhombicosidodecahedron() //J72
// addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
// addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
// addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
// #local raxis=vnormalize(<tau,-1,0>);
// rotate_vtxs(-raxis,36,-3.077)
// autobalance() autoface()
// #end
// #macro trigyrate_rhombicosidodecahedron() //J75
// addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
// addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
// addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
// #local raxis=vnormalize(<tau,-1,0>);
// rotate_vtxs(-raxis,36,-3.077)
// #local raxis=vnormalize(<-1,0,-tau>);
// rotate_vtxs(-raxis,36,-3.077)
// #local raxis=vnormalize(<-1,0,tau>);
// rotate_vtxs(-raxis,36,-3.077)
// autobalance() autoface()
// #end
////////////// sporadics
#macro snub_disphenoid() // J84
addpoint(<1,0,0>) #local EQTR1=npoints-1;
addpoint(<0,1,0>) #local EQTR2=npoints-1;
addpoint(<-1,0,0>) #local EQTR3=npoints-1;
addpoint(<0,-1,0>) #local EQTR4=npoints-1;
addpoint(<1,0,1>) #local NORTH1=npoints-1;
addpoint(<-1,0,1>) #local NORTH2=npoints-1;
addpoint(<0,1,-1>) #local SOUTH1=npoints-1;
addpoint(<0,-1,-1>) #local SOUTH2=npoints-1;
make_triangle(EQTR1,EQTR2,NORTH1) make_triangle(EQTR1,EQTR2,SOUTH1)
make_triangle(EQTR1,EQTR4,NORTH1) make_triangle(EQTR1,EQTR4,SOUTH2)
make_triangle(EQTR2,EQTR3,NORTH2) make_triangle(EQTR2,EQTR3,SOUTH1)
make_triangle(EQTR3,EQTR4,NORTH2) make_triangle(EQTR3,EQTR4,SOUTH2)
addedge(NORTH1,NORTH2,1)
addedge(SOUTH1,SOUTH2,1)
optimise(100,0.000001)
autobalance() autoface()
#end
#macro snub_square_antiprism() // J85
addpoint(<sq2,0,0>) #local E1=npoints-1;
addpoint(<1,1,0>) #local E2=npoints-1;
addpoint(<0,sq2,0>) #local E3=npoints-1;
addpoint(<-1,1,0>) #local E4=npoints-1;
addpoint(<-sq2,0,0>) #local E5=npoints-1;
addpoint(<-1,-1,0>) #local E6=npoints-1;
addpoint(<0,-sq2,0>) #local E7=npoints-1;
addpoint(<1,-1,0>) #local E8=npoints-1;
addpoint(<.5,.5,1>) #local N1=npoints-1;
addpoint(<-.5,.5,1>) #local N2=npoints-1;
addpoint(<-.5,-.5,1>) #local N3=npoints-1;
addpoint(<.5,-.5,1>) #local N4=npoints-1;
addpoint(<1/sq2,0,-1>) #local S1=npoints-1;
addpoint(<0,1/sq2,-1>) #local S2=npoints-1;
addpoint(<-1/sq2,0,-1>) #local S3=npoints-1;
addpoint(<0,-1/sq2,-1>) #local S4=npoints-1;
make_triangle(E1,E2,N1) make_triangle(E1,E2,S1)
make_triangle(E2,E3,N1) make_triangle(E2,E3,S2)
make_triangle(E3,E4,N2) make_triangle(E3,E4,S2)
make_triangle(E4,E5,N2) make_triangle(E4,E5,S3)
make_triangle(E5,E6,N3) make_triangle(E5,E6,S3)
make_triangle(E6,E7,N3) make_triangle(E6,E7,S4)
make_triangle(E7,E8,N4) make_triangle(E7,E8,S4)
make_triangle(E8,E1,N4) make_triangle(E8,E1,S1)
addedge(N1,N2,1) addedge(N2,N3,1) addedge(N1,N3,sq2)
addedge(N3,N4,1) addedge(N4,N1,1) addedge(N2,N4,sq2)
addedge(S1,S2,1) addedge(S2,S3,1) addedge(S1,S3,sq2)
addedge(S3,S4,1) addedge(S4,S1,1) addedge(S2,S4,sq2)
optimise(400,0.00000001)
autobalance()
autoface()
#end
#macro sphenocoronae(n) // J86 & J87
addpoint(<1,0,0>) #local E1=npoints-1;
addpoint(<.5,1,0>) #local E2=npoints-1;
addpoint(<-.5,1,0>) #local E3=npoints-1;
addpoint(<-1,0,0>) #local E4=npoints-1;
addpoint(<-.5,-1,0>) #local E5=npoints-1;
addpoint(<.5,-1,0>) #local E6=npoints-1;
addpoint(<.5,0,1>) #local N1=npoints-1;
addpoint(<-.5,0,1>) #local N2=npoints-1;
addpoint(<0,.5,-1>) #local S1=npoints-1;
addpoint(<0,-.5,-1>) #local S2=npoints-1;
make_lune(E1,E2,E3,E4,N2,N1)
make_lune(E4,E5,E6,E1,N1,N2)
make_triangle(E1,E2,S1) make_triangle(E2,E3,S1) make_triangle(E3,E4,S1)
make_triangle(E4,E5,S2) make_triangle(E5,E6,S2) make_triangle(E6,E1,S2)
addedge(S1,S2,1)
optimise(400,0.00000001)
#if(n=87) augment(4,points[E2],points[E3],points[N2]) #end
autobalance()
autoface()
#end
#macro sphenocorona() // J86
sphenocoronae(86)
#end
#macro augmented_sphenocorona() // J87
sphenocoronae(87)
#end
#macro augmented_sphenocorona_old() // J87
addpoint(<1,0,0>) #local E1=npoints-1;
addpoint(<.5,1,0>) #local E2=npoints-1;
addpoint(<-.5,1,0>) #local E3=npoints-1;
addpoint(<-1,0,0>) #local E4=npoints-1;
addpoint(<-.5,-1,0>) #local E5=npoints-1;
addpoint(<.5,-1,0>) #local E6=npoints-1;
addpoint(<.5,0,1>) #local N1=npoints-1;
addpoint(<-.5,0,1>) #local N2=npoints-1;
addpoint(<0,.5,-1>) #local S1=npoints-1;
addpoint(<0,-.5,-1>) #local S2=npoints-1;
make_lune(E1,E2,E3,E4,N2,N1)
make_lune(E4,E5,E6,E1,N1,N2)
make_triangle(E1,E2,S1) make_triangle(E2,E3,S1) make_triangle(E3,E4,S1)
make_triangle(E4,E5,S2) make_triangle(E5,E6,S2) make_triangle(E6,E1,S2)
addedge(S1,S2,1)
addpoint(<0,1,1>) #local A=npoints-1;
make_triangle(A,E2,E3) make_triangle(A,N2,N1)
optimise(400,0.00000001)
autobalance()
autoface()
#end
#macro sphenomegacorona() // J88
addpoint(<1.3,0,0.1>) #local E1=npoints-1;
addpoint(<.5,.6,0>) #local E2=npoints-1;
addpoint(<-.5,.6,0>) #local E3=npoints-1;
addpoint(<-1.3,0,0.1>) #local E4=npoints-1;
addpoint(<-.5,-.6,0>) #local E5=npoints-1;
addpoint(<.5,-.6,0>) #local E6=npoints-1;
addpoint(<.5,0,.7>) #local N1=npoints-1;
addpoint(<-.5,0,.7>) #local N2=npoints-1;
addpoint(<0,.5,-.9>) #local S1=npoints-1;
addpoint(<-.8,0,-.8>) #local S2=npoints-1;
addpoint(<0,-.5,-.9>) #local S3=npoints-1;
addpoint(<.8,0,-.8>) #local S4=npoints-1;
make_lune(E1,E2,E3,E4,N2,N1)
make_lune(E4,E5,E6,E1,N1,N2)
make_triangle(E1,E2,S4) make_triangle(E2,E3,S1) make_triangle(E3,E4,S2)
make_triangle(E4,E5,S2) make_triangle(E5,E6,S3) make_triangle(E6,E1,S4)
make_triangle(S1,S2,S3) make_triangle(S3,S4,S1)
optimise(400,0.000001)
// showvtxs()
autobalance()
autoface()
#end
#macro hebesphenomegacorona() // J89
addpoint(< 1.10, 0.00, 0.20>) #local E1=npoints-1;
addpoint(< 0.50, 0.72,-0.15>) #local E2=npoints-1;
addpoint(<-0.50, 0.72,-0.15>) #local E3=npoints-1;
addpoint(<-1.10, 0.00, 0.20>) #local E4=npoints-1;
addpoint(<-0.50,-0.72,-0.15>) #local E5=npoints-1;
addpoint(< 0.50,-0.72,-0.15>) #local E6=npoints-1;
addpoint(< 0.50, 0.50, 0.83>) #local N1=npoints-1;
addpoint(<-0.50, 0.50, 0.83>) #local N2=npoints-1;
addpoint(<-0.50,-0.50, 0.83>) #local N3=npoints-1;
addpoint(< 0.50,-0.50, 0.83>) #local N4=npoints-1;
addpoint(< 0.00, 0.50,-0.99>) #local S1=npoints-1;
addpoint(<-0.84, 0.00,-0.76>) #local S2=npoints-1;
addpoint(< 0.00,-0.50,-0.99>) #local S3=npoints-1;
addpoint(< 0.84, 0.00,-0.76>) #local S4=npoints-1;
make_lune(E1,E2,E3,E4,N2,N1)
make_lune(E4,E5,E6,E1,N4,N3)
make_lune(E1,N1,N2,E4,N3,N4)
make_triangle(E1,E2,S4) make_triangle(E2,E3,S1) make_triangle(E3,E4,S2)
make_triangle(E4,E5,S2) make_triangle(E5,E6,S3) make_triangle(E6,E1,S4)
make_triangle(S1,S2,S3)
make_triangle(S3,S4,S1)
optimise(400,0.000001)
showvtxs()
autobalance()
autoface()
#end
#macro disphenocingulum() // J90
addpoint(< 0.00, 0.50, 1.10>) #local NN1=npoints-1;
addpoint(< 0.00,-0.50, 1.10>) #local NN2=npoints-1;
addpoint(< 0.00, 1.12, 0.33>) #local N1=npoints-1;
addpoint(< 0.77, 0.50, 0.46>) #local N2=npoints-1;
addpoint(< 0.77,-0.50, 0.46>) #local N3=npoints-1;
addpoint(< 0.00,-1.12, 0.33>) #local N4=npoints-1;
addpoint(<-0.77,-0.50, 0.46>) #local N5=npoints-1;
addpoint(<-0.77, 0.50, 0.46>) #local N6=npoints-1;
addpoint(< 0.50, 0.77,-0.46>) #local S1=npoints-1;
addpoint(< 1.12, 0.00,-0.33>) #local S2=npoints-1;
addpoint(< 0.50,-0.77,-0.46>) #local S3=npoints-1;
addpoint(<-0.50,-0.77,-0.46>) #local S4=npoints-1;
addpoint(<-1.12, 0.00,-0.33>) #local S5=npoints-1;
addpoint(<-0.50, 0.77,-0.46>) #local S6=npoints-1;
addpoint(< 0.50, 0.00,-1.10>) #local SS1=npoints-1;
addpoint(<-0.50, 0.00,-1.10>) #local SS2=npoints-1;
make_lune(N1,N2,N3,N4,NN2,NN1)
make_lune(N4,N5,N6,N1,NN1,NN2)
make_lune(S2,SS1,SS2,S5,S6,S1)
make_lune(S2,S3,S4,S5,SS2,SS1)
make_triangle(N1,S1,N2)
make_triangle(N2,S2,N3)
make_triangle(N3,S3,N4)
make_triangle(N4,S4,N5)
make_triangle(N5,S5,N6)
make_triangle(N6,S6,N1)
optimise(400,0.000001)
showvtxs()
autobalance()
autoface()
#end
#macro bilunabirotunda() // J91
// start with icosahedron
addevenpermssgn(<0,1,tau>,<0,1,1>)
// showvtxs()
// trim back to 8 vertices
drop_halfspace(<-1,-tau,0>,-tau)
drop_halfspace(<-1,tau,0>,-tau)
drop_halfspace(<1,0,0>,-1)
// now shift all vertices into halfspace x >= 0, and mirror
#local i=0;#local minx=999;
#while (i<npoints)
#local minx=min(minx,points[i].x);
//#if (minx>points[i].x) #local minx=points[i].x; #end
#local i=i+1;
#end // (while loop)
#local i=0; #local np=npoints;
#while (i<np)
#declare points[i]=points[i]+<-minx,0,0>;
#if (points[i].x>0) addpoint(<-points[i].x,points[i].y,points[i].z>) #end
#local i=i+1;
#end // (while loop)
autoface()
#end
#macro triangular_hebesphenorotunda() // J91
// Coords found by taking 7 vtxs of an icosahedron, placing one vtx
// at origin, which is centre of the one hexagonal face.
addevenperms( <1,tau,0>-<tau,0,1>)
addevenperms( <0,1,tau>-<tau,0,1>)
addevenperms( <-1,tau,0>-<tau,0,1>)
addevenperms( <-tau,0,1>-<tau,0,1>)
addevenperms( <0,1,-tau>-<tau,0,1>)
addevenperms(-<1,tau,0>-<tau,0,1>)
autobalance()
autoface()
#end
//<<<<<<<<<<<<<<<<< added AGK [20041101]
#declare points=array[1000];
#declare tpoints=array[1000];
#declare npoints=0;
#declare faces=array[1000];
#declare nfaces=0;
#macro addpoint(a)
#declare points[npoints]=a;
#declare npoints=npoints+1;
#end
#macro addevenperms(a)
addpoint(a)
addpoint(<a.y,a.z,a.x>)
addpoint(<a.z,a.x,a.y>)
#end
#macro addperms(a)
addevenperms(a)
addevenperms(<a.x,a.z,a.y>)
#end
#macro addpointssgn(a,s)
addpoint(a)
#if(s.x) addpointssgn(a*<-1,1,1>,s*<0,1,1>) #end
#if(s.y) addpointssgn(a*<1,-1,1>,s*<0,0,1>) #end
#if(s.z) addpoint(a*<1,1,-1>) #end
#end
#macro addevenpermssgn(a,s)
addpointssgn(a,s)
addpointssgn(<a.y,a.z,a.x>,<s.y,s.z,s.x>)
addpointssgn(<a.z,a.x,a.y>,<s.z,s.x,s.y>)
#end
#macro addpermssgn(a,s)
addevenpermssgn(a,s)
addevenpermssgn(<a.x,a.z,a.y>,<s.x,s.z,s.y>)
#end
#macro addpointsevensgn(a)
addpoint(a)
addpoint(a*<-1,-1,1>)
addpoint(a*<-1,1,-1>)
addpoint(a*<1,-1,-1>)
#end
#macro addevenpermsevensgn(a)
addevenperms(a)
addevenperms(a*<-1,-1,1>)
addevenperms(a*<-1,1,-1>)
addevenperms(a*<1,-1,-1>)
#end
#macro addpermsaltsgn(a)
addevenpermsevensgn(a)
addevenpermsevensgn(<a.x,a.z,-a.y>)
#end
/*#macro addevenpermssgn(a,s) //Calls addevenperms with, for each 1 in s, a.{x,y,z} replaced with {+,-}a.{x,y,z}
addevenperms(a)
#if(s.x) addevenpermssgn(a*<-1,1,1>,s*<0,1,1>) #end
#if(s.y) addevenpermssgn(a*<1,-1,1>,s*<0,0,1>) #end
#if(s.z) addevenperms(a*<1,1,-1>) #end
#end*/
#macro addface(d,l)
#local a=vnormalize(d)/l;
#local f=1;
#local n=0; #while(n<nfaces-.5)
#if(vlength(faces[n]-a)<0.00001) #local f=0; #end
#local n=n+1; #end
#if(f)
#declare faces[nfaces]=a;
#declare nfaces=nfaces+1;
#end
#end
#macro dual()
#declare temp=faces;
#declare faces=points;
#declare points=temp;
#declare temp=nfaces;
#declare nfaces=npoints;
#declare npoints=temp;
#end
#macro autoface() //WARNING: ONLY WORKS IF ALL EDGES HAVE EQUAL LENGTH
//Find edge length
#declare elength=1000;
#local a=0; #while(a<npoints-.5) #local b=0; #while(b<npoints-.5)
#local c=vlength(points[a]-points[b]); #if(c>0.00001 & c<elength) #local elength=c; #end
#local b=b+1; #end #local a=a+1; #end
#debug concat("elength=",str(elength,9,9),"\n") showvtxs()
//Find planes
//#macro planes()
#local a=0; #while(a<npoints-.5)
#local b=a+1; #while(b<npoints-.5)
#if(vlength(points[a]-points[b])<elength+0.00001) #local c=b+1; #while(c<npoints-.5)
#if(vlength(points[a]-points[c])<elength+0.00001)
#local n=vnormalize(vcross(points[b]-points[a],points[c]-points[a]));
#local d=vdot(n,points[a]);
#if(d<0) #local n=-n; #local d=-d; #end
#local f=1;
#local e=0; #while(e<npoints-.5)
#if(vdot(n, points[e])>d+0.00001) #local f=0; #end
#local e=e+1; #end
#if(f)
#declare ld=d;
addface(n,d) //plane { n, d }
#end
#end
#local c=c+1; #end #end
#local b=b+1; #end
#local a=a+1; #end
#end
This_shape_will_be_drawn()
//Random rotations are (hopefully) equally distributed...
#declare rot1=rand(rotation)*pi*2;
#declare rot2=acos(1-2*rand(rotation));
#declare rot3=(rand(rotation)+clock)*pi*2;
#macro dorot()
rotate rot1*180/pi*y
rotate rot2*180/pi*x
rotate rot3*180/pi*y
#end
// drawit()
#if(1)
//Scale shape to fit in unit sphere
#local b=0;
#local a=0; #while(a<npoints-.5)
#local c=vlength(points[a]); #if(c>b) #local b=c; #end
#local a=a+1; #end
#local a=0; #while(a<npoints-.5)
#local points[a]=points[a]/b;
#local a=a+1; #end
#local a=0; #while(a<nfaces-.5)
#local faces[a]=faces[a]*b;
#local a=a+1; #end
#end
//Draw edges
#macro addp(a)
#declare p[np]=a;
#declare np=np+1;
#end
#local a=0; #while(a<nfaces-.5)
#declare p=array[20];
#declare np=0;
#local b=0; #while(b<npoints-.5)
#if(vdot(faces[a],points[b])>1-0.00001) addp(b) #end
#local b=b+1; #end
#local c=0; #while(c<np-.5)
#local d=0; #while(d<np-.5) #if(p[c]<p[d]-.5)
#local f=1;
#local e=0; #while(e<np-.5) #if(e!=c & e!=d & vdot(vcross(points[p[c]],points[p[d]]),points[p[e]])<0)
#local f=0;
#end #local e=e+1; #end
#if(f)
object {
cylinder { points[p[c]], points[p[d]], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#end #end
#local d=d+1; #end
#local c=c+1; #end
#local a=a+1; #end
/*#local a=0; #while(a<npoints-.5)
#local b=a+1; #while(b<npoints-.5)
#if(vlength(points[a]-points[b])<elength+0.00001)
object {
cylinder { points[a], points[b], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#end
#local b=b+1; #end
#local a=a+1; #end*/
//>>>>>>>>>>>>>>>>> changed AGK [20041101]
//Draw points
#if (1)
#local a=0; #while(a<npoints-.5)
object {
sphere { points[a], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#local a=a+1; #end
#else
#local a=0; #while(a<npoints-.5)
#local i=0;
#while(i<=a)
object {
sphere { (1+i/10)*points[a], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#local i=i+1;
#end
#local a=a+1; #end
#end
//<<<<<<<<<<<<<<<<< changed AGK [20041101]
#if(notwireframe)
//Draw planes
object {
intersection {
#local a=0; #while(a<nfaces-.5)
plane { faces[a], 1/vlength(faces[a]) }
#local a=a+1; #end
//planes()
//sphere { <0,0,0>, 1 }
//sphere { <0,0,0>, ld+.01 inverse }
dorot()
}
pigment { colour rgbt <.8,.8,.8,.4> }
finish { ambient 0 diffuse 1 phong flashiness #if(withreflection) reflection { .2 } #end }
//interior { ior 1.5 }
photons {
target on
refraction on
reflection on
collect on
}
}
#end
// CCC Y Y PP
// C Y Y P P
// C Y PP
// C Y P
// CCC Y P
#local a=0;
#while(a<11.0001)
light_source { <4*sin(a*pi*2/11), 5*cos(a*pi*6/11), -4*cos(a*pi*2/11)> colour (1+<sin(a*pi*2/11),sin(a*pi*2/11+pi*2/3),sin(a*pi*2/11+pi*4/3)>)*2/11 }
// light_source { <4*sin(a*pi*2/11), 5*cos(a*pi*6/11), -4*cos(a*pi*2/11)>
// colour (1+<sin(a*pi*2/11),sin(a*pi*2/11+pi*2/3),sin(a*pi*2/11+pi*4/3)>)*2/11 }
#local a=a+1;
#end
background { color <1,1,1> }
#if (0) // default framing vs auto-framing
camera {
perspective
location <0,0,0>
direction <0,0,1>
right x/2
up y/2
sky <0,1,0>
location <0,0,-4.8>
// location <0,0,-10>
look_at <0,0,0>
}
#else
// some auto-framing. Not for animated versions.
#declare camera_loc=<0,0,-4.8>;
#declare max_elevation=0; #declare max_bearing=0;
#declare i=0;
#while (i<npoints)
#declare sighting=points[i];
#declare sighting=vaxis_rotate(sighting,y,rot1*180/pi);
#declare sighting=vaxis_rotate(sighting,x,rot2*180/pi);
#declare sighting=vaxis_rotate(sighting,y,rot3*180/pi);
#declare sighting=sighting-camera_loc;
#declare elevation=sighting.y/sighting.z;
#declare bearing=sighting.x/sighting.z;
#declare max_elevation = max(max_elevation,abs(elevation));
#declare max_bearing = max(max_bearing,abs(bearing));
// sphere{ (camera_loc+<bearing,elevation,1>*10), 0.2
// pigment{ colour rgb <1,0,1> } }
#declare i=i+1;
#end
#debug concat("Maximum: Elevation = ",str(max_elevation,4,4)," Bearing = ",str(max_bearing,4,4),"\n")
#if(1) // 1:1 aspect ratio
#declare max_bearing = max(max_elevation,max_bearing); #declare max_elevation=max_bearing;
#end
#if(1) // 5% border
#declare max_bearing=1.05*max_bearing;
#declare max_elevation=1.05*max_elevation;
#end
camera {
perspective
location camera_loc
direction <0,0,.5>
right x*max_bearing
up y*max_elevation
}
#end
global_settings {
max_trace_level 40
photons {
count 200000
autostop 0
}
}