Talk:Polytope compound

I added images for the 5 regular compounds, and added 2 simplest dual-compounds of regular polyhedra. I didn't add any text about the mixed compounds. Obviously there's many more possible, but this is a good minimum. Tom Ruen 05:57, 22 October 2005 (UTC)

What about the great dodecahedron {5, 5/2} and small stellated dodecahedron {5/2, 5}? Does the latter swallow the former? —Tamfang 05:52, 4 September 2006 (UTC)

I think so, although I don't remember how I knew that. Tom Ruen 16:29, 4 September 2006 (UTC)

It does, see Mathworld. Double sharp (talk) 05:26, 16 August 2009 (UTC)

Or see the picture: . Double sharp (talk) 07:16, 23 March 2013 (UTC)

synonyms

Sources for the names chiro-icosahedron and icosiicosahedron and rhombihedron? —Tamfang (talk) 02:14, 16 May 2011 (UTC)

They're from Richard Klitzing's website. Double sharp (talk) 04:38, 25 December 2011 (UTC)

The irony, it burns! —Tamfang (talk) 22:22, 13 January 2015 (UTC)

Dual compounds of Regular compounds

I think Regular compounds can form their Dual compounds further, following same rule:

Two tetrahedra forms itself;

Five tetrahedra form Ten tetrahedra;

Ten tetrahedra forms itself;

Five cubes and Five octahedra should form something like Five Compounds of cube and octahedron. It may become the last one of the top class. --Haojian (talk) 09:38, 11 March 2019 (UTC)

and Five Compounds of cube and octahedron may lead to its hull (five Rhombic dodecahedra) and its core (five cuboctahedra)--Haojian (talk) 08:45, 16 March 2019 (UTC)

Is there a reason Polytope_compound#Uniform_compounds are not in numerical order?

I'm no expert on this at all... but it seems odd that the images are in a random order rather than being listed from 2 - 19, is there some reason for this that I'm unaware of, or would sorting them be appropriate? JeffUK 09:06, 27 January 2023 (UTC)

Hey Jeff! Yes, they are organized according to their symmetries 20-25 purely prismatic, 26-45 prismatic symmetry embedded in octahedral/icosahedral symmetries, ... so forth. Radlrb (talk) 09:48, 27 January 2023 (UTC)

Regular compound definition does not match source

The definition provided for regular compounds does not match the one given by Coxeter in Regular polytopes, a source cited in the section. The article gives the definition as:

A regular polyhedral compound can be defined as a compound which, like a regular polyhedron, is vertex-transitive, edge-transitive, and face-transitive.

I'm not going to reproduce any text from Coxeter exactly, but Coxeter's definition is in my own words:

A regular compound is a compound of regular polytopes, such that its vertices are the vertices of a regular polytope or its facet hyperplanes are parallel the facet hyperplanes of a regular polytope.

In the paper New regular compounds of 4-polytopes McMullen gives a similar definition to Coxeter. I have not found any source corroborating the definition given in this article. It does seem likely that all three definitions (McMullen's, Coxeters and the mystery definition used here) give the same 5 regular polyhedra, but they do not generalize equally to higher rank polytopes, and even so including it is WP:OR.

I've added a dispute tag to the section. If someone can come up with a source supporting this definition, the article can be adjusted to reflect the different uses of the term, otherwise I will replace it with a definition which can be sourced. AquitaneHungerForce (talk) AquitaneHungerForce (talk) 16:23, 28 November 2023 (UTC)

Yeah, I agree this should be changed. AFAICS, neither Coxeter nor McMullen's enumeration of regular polychoron compounds agrees with the obvious generalisation of the WP definition. Double sharp (talk) 09:04, 12 October 2024 (UTC)