Acronym | ... |
Name | tetrahedral - 2n-prismantiprismoid |
Circumradius | ... |
Face vector | 16n, 64n, 100n+8, 64n+12, 12n+6 |
Especially | s4x2o3o4s (n=2) s6x2o3o4s (n=3) |
Confer |
|
These isogonal polytera are obtained by hemiation of 4n-cube duoprism. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.
Incidence matrix according to Dynkin symbol
s2nx2o3o4s (n > 1) demi( . . . . . ) | 16n | 1 3 3 1 | 1 3 6 9 3 | 3 3 1 9 4 3 | 3 1 1 4 -------------------+-----+---------------+-------------------+----------------------+----------- demi( . x . . . ) | 2 | 8n * * * | 1 3 3 0 0 | 3 0 0 6 0 3 | 3 0 1 3 x s . 2 . s | 2 | * 24n * * | 0 0 2 4 0 | 1 2 0 4 2 0 | 2 1 0 2 q . . . o4s | 2 | * * 24n * | 0 1 0 2 2 | 0 1 1 2 2 2 | 1 1 1 2 q sefa( s2nx . . . ) | 2 | * * * 8n | 1 0 3 0 0 | 3 0 0 3 0 0 | 3 0 0 1 y = x(4n,3) -------------------+-----+---------------+-------------------+----------------------+----------- s2nx . . . | 2n | n 0 0 n | 8 * * * * | 3 0 0 0 0 0 | 3 0 0 0 xny . x 2 o4s | 4 | 2 0 2 0 | * 12n * * * | 0 0 0 2 0 2 | 1 0 1 2 x2q sefa( s2nx 2 . s ) | 4 | 1 2 0 1 | * * 24n * * | 1 0 0 2 0 0 | 2 0 0 1 xy&#q sefa( s . 2 o4s ) | 3 | 0 2 1 0 | * * * 48n * | 0 1 0 1 1 0 | 1 1 0 1 q3o sefa( . . o3o4s ) | 3 | 0 0 3 0 | * * * * 16n | 0 0 1 0 1 1 | 0 1 1 1 q3o -------------------+-----+---------------+-------------------+----------------------+----------- s2nx 2 . s | 4n | 2n 2n 0 2n | 2 0 2n 0 0 | 12 * * * * * | 2 0 0 0 xy-2n-yx&#q (di-n-gonal trapezoprism) s . 2 o4s | 4 | 0 4 2 0 | 0 0 0 4 0 | * 12n * * * * | 1 1 0 0 q-tet . . o3o4s | 4 | 0 0 6 0 | 0 0 0 0 4 | * * 4n * * * | 0 1 1 0 q-tet sefa( s2nx 2 o4s ) | 6 | 2 4 2 1 | 0 1 2 2 0 | * * * 24n * * | 1 0 0 1 yx2oq&#q (wedge-like trip variant) sefa( s 2 o3o4s ) | 4 | 0 3 3 0 | 0 0 0 3 1 | * * * * 16n * | 0 1 0 1 q-tet sefa( . x2o3o4s ) | 6 | 3 0 6 0 | 0 3 0 0 2 | * * * * * 8n | 0 0 1 1 x q3o (trip variant) -------------------+-----+---------------+-------------------+----------------------+----------- s2nx 2 o4s | 8n | 4n 8n 4n 4n | 4 2n 8n 8n 0 | 4 2n 0 4n 0 0 | 6 * * * 2-2n prismantiprismoid s 2 o3o4s | 8 | 0 12 12 0 | 0 0 0 24 8 | 0 6 2 0 8 0 | * 2n * * q-hex . x2o3o4s | 8 | 4 0 12 0 | 0 6 0 0 8 | 0 0 2 0 0 4 | * * 2n * x q3o3o (tepe variant) sefa( s2nx2o3o4s ) | 8 | 3 6 6 1 | 0 3 3 6 2 | 0 0 0 3 2 1 | * * * 8n yx2oq3oo&#q (tepe variant) starting figure: x2nx o3o4x
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