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)[reply]

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)[reply]

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)[reply]

Its due to the tetrahedral symmetry construction. alternation(t{3,4}×{} =t_0,1{3,4}×{})=h_0,1{3,4}), alternation {t_0,1,2{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 h_0,1{3,4,3}, so we might say semisnub octahedral prism for h_0,1{3,4,2}? Tom Ruen (talk) 20:19, 26 July 2013 (UTC)[reply]

I like this! Double sharp (talk) 04:29, 27 July 2013 (UTC)[reply]

Shoot, mistake: alternation t_0,1{3,4}×{} = alternation t_0,1,3{3,4,2} = h_0,1,3{3,4,2} NOT h_0,1{3,4}x{}. Tom Ruen (talk) 04:35, 27 July 2013 (UTC)[reply]

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)[reply]