Table expanded a bit from [1], trying to sort out the Bowers naming system.
General (selective)
editPrefix | Coxeter-Dynkin diagram {p,q,r,s,t} |
Bowers adjectives | Johnson adjectives |
---|---|---|---|
t0 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
regular | |
t1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
rectified | |
t2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-rectified | |
t3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-rectified | |
t4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
quadri-rectified | |
t5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
quinti-rectified | |
t6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
sexti-rectified | |
t7 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
septi-rectified | |
t8 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
octi-rectified | |
t9 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
noni-rectified | |
t10 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
deci-rectified | |
t11 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
unideci-rectified | |
t0,1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
truncated | |
t0,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) rhombated | cantellated / canti- |
t0,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) prismated / prismato- | runcinated / runci- |
t0,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) cellated / celli- | stericated / steri- |
t0,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) terated / tera- | [pentellated / penti-] |
t0,6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) petated / peta- | [hexicated / hexi-] |
t0,7 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) exated / exa- | [heptellated / hepti-] |
t0,8 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) zettated / zetta- | [octellated / octi-] |
t0,9 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) yottated / yotta- | [ennecated / enni-] |
t1,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-truncated | |
t1,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) bi-rhombated | bi-cantellated |
t1,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) bi-prismated | bi-runcinated |
t1,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) bi-cellated | bi-stericated |
t2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-truncated | |
t2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) tri-rhombated | tri-cantellated |
t2,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) tri-prismated | tri-runcinated |
t3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
quadri-truncated | |
t3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) quadri-rhombated | quadri-cantellated |
t4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
quinti-truncated | |
t0,1,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great rhombated | cantitruncated |
t0,1,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
prismatotruncated | runcitruncated |
t0,1,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cellitruncated | steritruncated |
t0,1,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teratruncated | pentitruncated |
t0,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
prismatorhombated | runcicantellated |
t0,2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) cellirhombated | stericantellated |
t0,2,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) terarhombated | penticantellated |
t0,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
celliprismated | steriruncinated |
t0,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teraprismated | pentiruncinated |
t0,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teracellated | pentistericated |
t1,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-rhombated | bi-cantitruncated |
t1,2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-prismatotruncated | bi-runcitruncated |
t1,2,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-cellitruncated | bi-steritruncated |
t1,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-prismatorhombated | bi-runcicantellated |
t1,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-cellirhombated | bi-stericantellated |
t1,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-celliprismated | bi-steriruncinated |
t2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great tri-rhombated | tri-cantitruncated |
t2,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-prismatotruncated | tri-runcitruncated |
t2,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-prismatorhombated | tri-runcicantellated |
t3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great quadri-rhombated | quadri-cantitruncated |
t0,1,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great prismated | runcicantitruncated |
t0,1,2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great cellirhombated | stericantitruncated |
t0,1,2,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great terarhombated | penticantitruncated |
t0,1,3,4 | ...![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
celliprismatotruncated | steriruncitruncated |
t0,1,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teraprismatotruncated | pentiruncitruncated |
t0,1,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teracellitruncated | pentisteritruncated |
t0,2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
celliprismatorhombated | steriruncicantellated |
t0,2,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teraprismatorhombated | pentiruncicantellated |
t0,2,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) teracellirhombated | pentistericantellated |
t1,2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-prismated | bi-runcicantitruncated |
t1,2,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-cellirhombated | bi-stericantitruncated |
t1,2,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-celliprismatotruncated | bi-steriruncitruncated |
t1,3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-celliprismatorhombated | bi-steriruncicantellated |
t2,3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great tri-prismated | tri-runcicantitruncated |
t0,1,2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great cellated | steriruncicantitruncated |
t0,1,2,3,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great teraprismated | pentiruncicantitruncated |
t0,1,2,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great teracellirhombated | pentistericantitruncated |
t0,1,3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teracelliprismatotruncated | pentisteriruncitruncated |
t0,2,3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
teracelliprismatorhombated | pentisteriruncicantellated |
t1,2,3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-cellated | bi-steriruncicantitruncated |
t0,1,2,3,4,5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great terated | pentisteriruncicantitruncated |
t0,last | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
expanded | |
tall | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
omnitruncated |
5-polytopes
editPrefix | Coxeter-Dynkin diagram {p,q,r,s} |
Bowers adjectives | Johnson adjectives |
---|---|---|---|
t0 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
regular | |
t1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
rectified | |
t2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-rectified | |
(*) t3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-rectified | |
(*) t4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
quadri-rectified | |
t0,1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
truncated | |
t0,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) rhombated | cantellated / canti- |
t0,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) prismated / prismato- | runcinated / runci- |
t0,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) cellated / celli- | stericated / steri- |
t1,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-truncated | |
t1,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) bi-rhombated | bi-cantellated |
(*) t1,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) bi-prismated | bi-runcinated |
(*) t2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-truncated | |
(*) t2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) tri-rhombated | tri-cantellated |
(*) t3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
quadri-truncated | |
t0,1,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great rhombated | cantitruncated |
t0,1,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
prismatotruncated | runcitruncated |
t0,1,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cellitruncated | steritruncated |
t0,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
prismatorhombated | runcicantellated |
t0,2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) cellirhombated | stericantellated |
(*) t0,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
celliprismated | steriruncinated |
t1,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-rhombated | bi-cantitruncated |
(*) t1,2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-prismatotruncated | bi-runcitruncated |
(*) t1,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-prismatorhombated | bi-runcicantellated |
(*) t2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great tri-rhombated | tri-cantitruncated |
t0,1,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great prismated | runcicantitruncated |
t0,1,2,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great cellirhombated | stericantitruncated |
(*) t0,1,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
celliprismatotruncated | steriruncitruncated |
(*) t0,2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
celliprismatorhombated | steriruncicantellated |
(*) t1,2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-prismated | bi-runcicantitruncated |
t0,1,2,3,4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great cellated | steriruncicantitruncated |
tall | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
omnitruncated |
4-polytopes
editPrefix | Coxeter-Dynkin diagram {p,q,r} |
Bowers adjectives | Johnson adjectives |
---|---|---|---|
t0 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
regular | |
t1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
rectified | |
(*) t2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-rectified | |
(*) t3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-rectified | |
t0,1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
truncated | |
t0,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) rhombated | cantellated / canti- |
t0,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) prismated / prismato- | runcinated / runci- |
t1,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
bi-truncated | |
(*) t1,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(small) bi-rhombated | bi-cantellated |
(*) t2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
tri-truncated | |
t0,1,2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great rhombated | cantitruncated |
t0,1,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
prismatotruncated | runcitruncated |
(*) t0,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
prismatorhombated | runcicantellated |
(*) t1,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great bi-rhombated | bi-cantitruncated |
t0,1,2,3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
great prismated | runcicantitruncated |
tall | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
omnitruncated |
3-polytopes
editPrefix | Coxeter-Dynkin diagram {p,q} |
Bowers adjectives | Johnson adjectives |
---|---|---|---|
t0 | ![]() ![]() ![]() ![]() ![]() |
regular | |
t1 | ![]() ![]() ![]() ![]() ![]() |
rectified | |
(*) t2 | ![]() ![]() ![]() ![]() ![]() |
bi-rectified | |
t0,1 | ![]() ![]() ![]() ![]() ![]() |
truncated | |
t0,2 | ![]() ![]() ![]() ![]() ![]() |
(small) rhombated | cantellated / canti- |
(*) t1,2 | ![]() ![]() ![]() ![]() ![]() |
bi-truncated | |
t0,1,2 | ![]() ![]() ![]() ![]() ![]() |
great rhombated | cantitruncated |
tall | ![]() ![]() ![]() ![]() ![]() |
omnitruncated |
2-polytopes
editPrefix | Coxeter-Dynkin diagram {p} |
Bowers adjectives | Johnson adjectives |
---|---|---|---|
t0 | ![]() ![]() ![]() |
regular | |
(*) t1 | ![]() ![]() ![]() |
rectified | |
t0,1 | ![]() ![]() ![]() |
truncated | |
tall | ![]() ![]() ![]() |
omnitruncated |
(*) unneeded - can be made by reverse construction
4-polytopes explicit
editPrefix | t0 | t1 | t2 | t3 | t0,1 | t0,2 | t0,3 | t1,2 | t1,3 | t2,3 | t0,1,2 | t0,1,3 | t0,2,3 | t1,2,3 | t0,1,2,3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Coxeter-Dynkin diagram {p,q,r} |
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Johnson prefix | regular | rectified | bi-rectified | tri-rectified | truncated | cantellated | runcinated | bi-truncated | bi-cantellated | tri-truncated | cantitruncated | runcitruncated | runcicantellated | bi-cantitruncated | runcicantitruncated (omnitruncated) |
Bowers prefix | regular | rectified | bi-rectified | tri-rectified | truncated | rhombated | prismated | bi-truncated | bi-rhombated | tri-truncated | great rhombated | prismatotruncated | prismatorhombated | great bi-rhombated | great prismated |
{3,3,3} | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Johnson | 5-cell | rectified 5-cell | bi-rectified 5-cell | tri-rectified 5-cell | truncated 5-cell | cantellated 5-cell | runcinated 5-cell | bi-truncated 5-cell | bi-cantellated 5-cell | tri-truncated 5-cell | cantitruncated 5-cell | runcitruncated 5-cell | runcicantellated 5-cell | bi-cantitruncated 5-cell | omnitruncated 5-cell |
Bowers | pentachoron (pen) |
rectified pentachoron (rap) |
bi-rectified pentachoron | tri-rectified pentachoron | truncated pentachoron (tip) |
rhombated pentachoron (srip) |
prismodecachoron (spid) |
decachoron (deca) |
bi-rhombated pentachoron | tri-truncated pentachoron | great rhombated pentachoron (grip) |
prismatotruncated pentachoron | prismatorhombated pentachoron (prip) |
great bi-rhombated pentachoron | great prismatodecachoron (gippid) |
{4,3,3} | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Johnson | 8-cell | rectified 8-cell | bi-rectified 8-cell | tri-rectified 8-cell | truncated 8-cell | cantellated 8-cell | runcinated 8-cell | bi-truncated 8-cell | bi-cantellated 8-cell | tri-truncated 8-cell | cantitruncated 8-cell | runcitruncated 8-cell | runcicantellated 8-cell | bi-cantitruncated 8-cell | omnitruncated 8-cell |
Bowers prefix | tesseract (tes) |
rectified tesseract (rit) |
bi-rectified tesseract rectified hexadecachoron [24-cell] |
tri-rectified tesseract hexadecachoron (hex) |
truncated tesseract (tat) |
rhombated tesseract (srit) |
prismatotesseractihexadecachoron (sidpith) |
tesseractihexadecachoron (tah) |
bi-rhombated tesseract rhombated hexadecachoron [r.24-cell] |
tri-truncated tesseract truncated hexadecachoron (thex) |
great rhombated tesseract (grit) |
prismatotruncated tesseract prismatorhombated hexadecachoron (proh) |
prismatorhombated tesseract (prit) |
great bi-rhombated tesseract great rhombated hexadecachoron [tr.24-cell] |
great prismatotesseractihexadecachoron (gidpith) |
{3,4,3} | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Johnson | 24-cell | rectified 24-cell | bi-rectified 24-cell | tri-rectified 24-cell | truncated 24-cell | cantellated 24-cell | runcinated 24-cell | bi-truncated 24-cell | bi-cantellated 24-cell | tri-truncated 24-cell | cantitruncated 24-cell | runcitruncated 24-cell | runcicantellated 24-cell | bi-cantitruncated 24-cell | omnitruncated 24-cell |
Bowers | icositetrachoron (ico) |
rectified icositetrachoron (rico) |
bi-rectified icositetrachoron | tri-rectified icositetrachoron | truncated icositetrachoron (tico) |
rhombated icositetrachoron (srico) |
prismotetracontaoctachoron (spic) |
tetracontaoctachoron (cont) |
bi-rhombated icositetrachoron | tri-truncated icositetrachoron | great rhombated icositetrachoron (grico) |
prismatotruncated icositetrachoron | prismatorhombated icositetrachoron (prico) |
great bi-rhombated icositetrachoron | great prismatotetracontaoctachoron (gippic) |
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Johnson | 120-cell | rectified 120-cell | bi-rectified 120-cell | tri-rectified 120-cell | truncated 120-cell | cantellated 120-cell | runcinated 120-cell | bi-truncated 120-cell | bi-cantellated 120-cell | tri-truncated 120-cell | cantitruncated 120-cell | runcitruncated 120-cell | runcicantellated 120-cell | bi-cantitruncated 120-cell | omnitruncated 120-cell |
Bowers prefix | hecatonicosachoron (hi) |
rectified hecatonicosachoron (rahi) |
bi-rectified hecatonicosachoron rectified hecatonicosachoron (rox) |
tri-rectified hecatonicosachoron hexacosichoron (ex) |
truncated hecatonicosachoron (thi) |
rhombated hecatonicosachoron (srahi) |
prismatohexacosihecatonicosachoron (sidpixhi) |
hexacosihecatonicosachoron (xhi) |
bi-rhombated hecatonicosachoron rhombated hexacosichoron (srix) |
tri-truncated hecatonicosachoron truncated hexacosichoron (tex) |
great rhombated hecatonicosachoron (grahi) |
prismatotruncated hecatonicosachoron prismatorhombated hexacosichoron (prix) |
prismatorhombated hecatonicosachoron (prahi) |
great bi-rhombated hecatonicosachoron great rhombated hexacosichoron (grix) |
great prismatohexacosihecatonicosachoron (gidpixhi) |
Johnson
edithttp://www.mathconsult.ch/lists/cgi/private/polyhedron/2006b/msg00273.html Higher Wythoffian operators (Johnson) *************************************************************** a.. From: "Norman Johnson" b.. Subject: Re: [Polyhedron] Higher Wythoffian operators c.. Date: Mon, 31 Jul 2006 12:25:03 -0400 d.. To: "Polyhedron Discussion List" <[email protected]> My names for the operations corresponding to ringing various nodes of a Coxeter diagram for a reflection group, thereby converting it into a Wythoff diagram for a uniform polytope or honeycomb, are as follows: t_0 original t_1 rectified t_2 birectified t_3 trirectified t_4 quadrirectified t_5 quintirectified . . . t_0,1 truncated t_1,2 bitruncated t_2,3 tritruncated . . . t_0,2 cantellated t_1,3 bicantellated t_2,4 tricantellated . . . t_0,3 runcinated t_1,4 biruncinated t_2,5 triruncinated . . . t_0,4 stericated t_1,5 bistericated t_2,6 tristericated . . . t_0,1,2 cantitruncated t_1,2,3 bicantitruncated t_2,3,4 tricantitruncated . . . t_0,1,3 runcitruncated t_1,2,4 biruncitruncated t_2,3,5 triruncitruncated . . . t_0,1,4 steritruncated t_1,2,5 bisteritruncated t_2,3,6 tristeritruncated . . . t_0,2,3 runcicantellated t_1,3,4 biruncicantellated t_2,4,5 triruncicantellated . . . t_0,1,2,3 runcicantitruncated t_1,2,3,4 biruncicantitruncated t_2,3,4,5 triruncicantitruncated If only the end nodes 0 and n are ringed, the term "expanded" can be used; when all nodes are ringed, the term is "omnitruncated." It should be borne in mind that these operations apply to regular figures and others whose Wythoff diagrams have their nodes numbered from left to right. I have not invented TOCID equivalents for n-polytopes or (n-1)- honeycombs with n > 4. Norman
Bowers
edithttp://www.mathconsult.ch/lists/cgi/private/polyhedron/2006b/msg00270.html *************************************************************** Subject: Re: [Polyhedron] Higher Wythoffian operators? nth order rectification and truncation? Date: Mon, 31 Jul 2006 17:48:11 +0200 Cc: [email protected] Tom asked for a rule based naming according to Wythoff's kaleidoscopical construction, i.e. a naming scheme which translates the decoration of Dynkin diagrams into names. This was given twice within the archive. One by Jonathan Bowers, one by Norman Johnson (the ndiffering names in parantheses). In what follows this system is given with respect to 6-dimensional linear Dynkin diagrams. Obviously, the higher the dimension, the more additional operators will be needed. [+pentellated/penti] 000001 - regular 000010 - rectated 000011 - truncated 000100 - birectated 000101 - small rhombated (cantellated) 000110 - bitruncated 000111 - great rhombated (cantitruncated) 001001 - small prismated (runcinated) 001010 - small birhombated (bicantellated) 001011 - prismatotruncated (runcitruncated) 001100 - tritruncated 001101 - prismatorhombated (runcicantellated) 001110 - great birhombated (bicantitruncated) 001111 - great prismated (runcicantitruncated) 010001 - small cellated (stericated) 010010 - small biprismated (biruncinated) 010011 - cellitruncated (steritruncated) 010101 - small cellirhombated (stericantellated) 011010 - biprismatorhombated (biruncitruncated) 010111 - great cellirhombated (stericantitruncated) 011001 - celliprismated (steriruncinated) 011011 - celliprismatotruncated (steriruncitruncated) 011101 - celliprismatorhombated (steriruncicantellated) 011110 - great biprismated (biruncicantitruncated) 011111 - great cellated (steriruncicantitruncated) 100001 - small terated [pentellated] 110001 - teracellated [pentitruncated] 101001 - small teraprismated [penticantellated] 111001 - teracelliprismated [penticantitruncated] 110101 - small teracellirhombated [pentiruncitruncated] 101101 - teraprismatorhombated [pentiruncicantellated] 101111 - great teraprismated [pentiruncicantitruncated] 110011 - teracellitruncated [pentisteritruncated] 110111 - great teracellirhombated (pentistericantitruncated] 111111 - great terated [pentisteriruncicantitruncated = omnitruncated]