Talk:Truncated octahedral prism
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snub question
[edit]It's clear that not all the cells of the alternation can simultaneously be regular; but is it established that, for example, the icosahedra cannot be made regular at the expense of some other cells? —Tamfang (talk) 04:35, 24 July 2013 (UTC)
- True, thought about that too. I copied from Richard Klitzing cell description which is apparently as an unadjusted alternated truncated octahedral prism. Tom Ruen (talk) 05:09, 24 July 2013 (UTC)
s2s3s3s demi( . . . . ) | 24 | 1 1 1 1 2 2 | 1 1 3 3 3 3 | 1 1 1 1 4 ----------------+----+-------------------+-----------------+----------- s2s . . | 2 | 12 * * * * * | 0 0 2 2 0 0 | 1 1 0 0 2 q s 2 s . | 2 | * 12 * * * * | 0 0 2 0 2 0 | 1 0 1 0 2 q s .2. s | 2 | * * 12 * * * | 0 0 0 2 2 0 | 0 1 1 0 2 q . s 2 s | 2 | * * * 12 * * | 0 0 0 2 0 2 | 0 1 0 1 2 q sefa( . s3s . ) | 2 | * * * * 24 * | 1 0 1 0 0 1 | 1 0 0 1 1 h sefa( . . s3s ) | 2 | * * * * * 24 | 0 1 0 0 1 1 | 0 0 1 1 1 h ----------------+----+-------------------+-----------------+----------- . s3s . | 3 | 0 0 0 0 3 0 | 8 * * * * * | 1 0 0 1 0 . . s3s | 3 | 0 0 0 0 0 3 | * 8 * * * * | 0 0 1 1 0 sefa( s2s3s . ) | 3 | 1 1 0 0 1 0 | * * 24 * * * | 1 0 0 0 1 sefa( s2s 2 s ) | 3 | 1 0 1 1 0 0 | * * * 24 * * | 0 1 0 0 1 sefa( s 2 s3s ) | 3 | 0 1 1 0 0 1 | * * * * 24 * | 0 0 1 0 1 sefa( . s3s3s ) | 3 | 0 0 0 1 1 1 | * * * * * 24 | 0 0 0 1 1 ----------------+----+-------------------+-----------------+----------- s2s3s . | 6 | 3 3 0 0 6 0 | 2 0 6 0 0 0 | 4 * * * * flattened trigonal antiprism s2s 2 s | 4 | 2 0 2 2 0 0 | 0 0 0 4 0 0 | * 6 * * * tetrahedron s 2 s3s | 6 | 0 3 3 0 0 6 | 0 2 0 0 6 0 | * * 4 * * flattened trigonal antiprism . s3s3s | 12 | 0 0 0 6 12 12 | 4 4 0 0 0 12 | * * * 2 * non-uniform icosahedron sefa( s2s3s3s ) | 4 | 1 1 1 1 1 1 | 0 0 1 1 1 1 | * * * * 24 irregular tetrahedron
is non-uniform (mere alternated faceting would make the first four kinds of edges of size q, the other two kinds of size h).
terminology is somewhat inconsistent
[edit]you call t{3,4}×{} a truncated octahedral prism, then call its alternation a snub tetrahedral [ANTI]prism. why does the former only apply to the second word while the latter applies to the second and third? Double sharp (talk) 14:33, 26 July 2013 (UTC)
- Its due to the tetrahedral symmetry construction. alternation(t{3,4}×{} =t0,1{3,4}×{})=h0,1{3,4}), alternation {t0,1,2{3,3}) = s{3,3}. So its an alternated truncated octahedral prism AND a snub tetrahedram [ANTI]prism. You could also say alternated omnitruncated tetrahedral prism. Conway calls the snub 24-cell a semi-snub 24-cell based on h0,1{3,4,3}, so we might say semisnub octahedral prism for h0,1{3,4,2}? Tom Ruen (talk) 20:19, 26 July 2013 (UTC)
- I like this! Double sharp (talk) 04:29, 27 July 2013 (UTC)
- Shoot, mistake: alternation t0,1{3,4}×{} = alternation t0,1,3{3,4,2} = h0,1,3{3,4,2} NOT h0,1{3,4}x{}. Tom Ruen (talk) 04:35, 27 July 2013 (UTC)
- Actually confusion deeper above, question should say snub tetrahedral antiprism (inserted correction [ANTI]) for s{3,3,2} to differentiate from s{3,3}x{} snub tetrahedral prism!!! Tom Ruen (talk) 05:45, 27 July 2013 (UTC)