Acronym | ... |
Name | tetrahedral - n-prismantiprismoid |
Circumradius | ... |
Face vector | 8n, 44n, 80n+8, 54n+12, 10n+6 |
Especially | s4o2o3o4s (n=2: hin) s6o2o3o4s (n=3) |
Confer |
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These isogonal polytera are obtained by hemiation of 2n-cube duoprism. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.
The exceptional case n=2 could be considered similarily, but the incidence matrices below will be different because of degeneracy. Then it becomes the hemiated pent (hin) and even happens to become uniform.
Incidence matrix according to Dynkin symbol
s2no2o3o4s (n > 2) demi( . . . . . ) | 8n | 6 3 2 | 1 9 18 3 | 3 6 1 12 8 | 3 2 5 -------------------+----+------------+--------------+-------------------+-------- s . 2 . s | 2 | 24n * * | 0 2 4 0 | 1 2 0 4 2 | 2 1 2 q . . . o4s | 2 | * 12n * | 0 0 4 2 | 0 2 1 2 4 | 1 2 2 q sefa( s2no . . . ) | 2 | * * 8n | 1 3 0 0 | 3 0 0 3 0 | 3 0 1 y = x(2n) -------------------+----+------------+--------------+-------------------+-------- s2no . . . | n | 0 0 n | 8 * * * | 3 0 0 0 0 | 3 0 0 yno sefa( s2no 2 . s ) | 3 | 2 0 1 | * 24n * * | 1 0 0 2 0 | 2 0 1 oy&#q sefa( s . 2 o4s ) | 3 | 2 1 0 | * * 48n * | 0 1 0 1 1 | 1 1 1 q3o sefa( . . o3o4s ) | 3 | 0 3 0 | * * * 8n | 0 0 1 0 2 | 0 2 1 q3o -------------------+----+------------+--------------+-------------------+-------- s2no 2 . s | 2n | 2n 0 2n | 2 2n 0 0 | 12 * * * * | 2 0 0 oy-n-yo&#q (n-ap variant) s . 2 o4s | 4 | 4 2 0 | 0 0 4 0 | * 12n * * * | 1 1 0 q-tet . . o3o4s | 4 | 0 6 0 | 0 0 0 4 | * * 2n * * | 0 2 0 q-tet sefa( s2no 2 o4s ) | 4 | 4 1 1 | 0 2 2 0 | * * * 24n * | 1 0 1 yo2oq&#q (disphenoid, tet variant) sefa( s 2 o3o4s ) | 4 | 3 3 0 | 0 0 3 1 | * * * * 16n | 0 1 1 q-tet -------------------+----+------------+--------------+-------------------+-------- s2no 2 o4s | 4n | 8n 1n 4n | 4 8n 8n 0 | 4 2n 0 4n 0 | 6 * * 2,n-dap s 2 o3o4s | 8 | 12 12 0 | 0 0 24 8 | 0 6 2 0 8 | * 2n * q-hex sefa( s2no2o3o4s ) | 5 | 6 3 1 | 0 3 6 1 | 0 0 0 3 2 | * * 8n yo2oq3oo&#q (tepe variant) starting figure: x2no o3o4x
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