Acronym | hextes |
Name | hexadecachoron-tesseract duoprism |
Circumradius | sqrt(3/2) = 1.224745 |
Volume | 1/6 = 0.166667 |
Face vector | 128, 640, 1472, 1920, 1496, 696, 184, 24 |
Confer |
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This polyzetton is a hemiation of octo, just as hocto. But this hemiation here is wrt. the first 4 coordinates only, while that of hocto is wrt. all 8 coordinates. – None the same this alternation here, when applied to octo, would produce different edge sizes, which, as shown below, can still be overcome. Therefore that relation to octo is just a combinatorical one, not a metrical one, in contrast to the case for hocto.
Incidence matrix according to Dynkin symbol
x3o3o4o o3o3o4x o3o3o4o o3o3o4o | 128 | 6 4 | 12 24 6 | 8 48 36 16 | 1 32 72 24 1 | 4 48 48 6 | 6 32 12 | 4 8 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x . . . . . . . | 2 | 384 * | 4 4 0 | 4 16 6 0 | 1 16 24 16 0 | 4 24 16 1 | 6 16 4 | 4 4 . . . . . . . x | 2 | * 256 | 0 6 3 | 0 12 18 3 | 0 8 36 18 1 | 1 24 36 4 | 3 24 12 | 3 8 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x3o . . . . . . | 3 | 3 0 | 512 * * | 2 4 0 0 | 1 8 6 0 0 | 4 12 4 0 | 6 8 1 | 4 2 x . . . . . . x | 4 | 2 2 | * 768 * | 0 4 3 0 | 0 4 12 3 0 | 1 12 12 1 | 3 12 4 | 3 4 . . . . . . o4x | 4 | 0 4 | * * 192 | 0 0 6 2 | 0 0 12 12 1 | 0 8 16 6 | 1 16 12 | 2 8 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x3o3o . . . . . ♦ 4 | 6 0 | 4 0 0 | 256 * * * | 1 4 0 0 0 | 4 6 0 0 | 6 4 0 | 4 1 x3o . . . . . x ♦ 6 | 6 3 | 2 3 0 | * 1024 * * | 0 2 3 0 0 | 1 6 3 0 | 3 6 1 | 3 2 x . . . . . o4x ♦ 8 | 4 8 | 0 4 2 | * * 576 * | 0 0 4 2 0 | 0 4 8 1 | 1 8 4 | 2 4 . . . . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * 64 | 0 0 0 6 1 | 0 0 12 6 | 0 8 12 | 1 8 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x3o3o4o . . . . ♦ 8 | 24 0 | 32 0 0 | 16 0 0 0 | 16 * * * * ♦ 4 0 0 0 | 6 0 0 | 4 0 x3o3o . . . . x ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | * 512 * * * | 1 3 0 0 | 3 3 0 | 3 1 x3o . . . . o4x ♦ 12 | 12 12 | 4 12 3 | 0 4 3 0 | * * 768 * * | 0 2 2 0 | 1 4 1 | 2 2 x . . . . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 192 * | 0 0 4 1 | 0 4 4 | 1 4 . . . . o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * 8 ♦ 0 0 0 6 | 0 0 12 | 0 8 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x3o3o4o . . . x ♦ 16 | 48 8 | 64 24 0 | 32 32 0 0 | 2 16 0 0 0 | 32 * * * | 3 0 0 | 3 0 x3o3o . . . o4x ♦ 16 | 24 16 | 16 24 4 | 4 16 6 0 | 0 4 4 0 0 | * 384 * * | 1 2 0 | 2 1 x3o . . . o3o4x ♦ 24 | 24 36 | 8 36 18 | 0 12 18 3 | 0 0 6 3 0 | * * 256 * | 0 2 1 | 1 2 x . . . o3o3o4x ♦ 32 | 16 64 | 0 32 48 | 0 0 24 16 | 0 0 0 8 2 | * * * 24 | 0 0 4 | 0 4 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x3o3o4o . . o4x ♦ 32 | 96 32 | 128 96 8 | 64 128 24 0 | 4 64 32 0 0 | 4 16 0 0 | 24 * * | 2 0 x3o3o . . o3o4x ♦ 32 | 48 48 | 32 72 24 | 8 48 36 4 | 0 12 24 6 0 | 0 6 4 0 | * 128 * | 1 1 x3o . . o3o3o4x ♦ 48 | 48 96 | 16 96 72 | 0 32 72 24 | 0 0 24 24 3 | 0 0 8 3 | * * 32 | 0 2 ----------------+-----+---------+-------------+-----------------+------------------+---------------+-----------+----- x3o3o4o . o3o4x ♦ 64 | 192 96 | 256 288 48 | 128 384 144 8 | 8 192 192 24 0 | 12 96 32 0 | 6 16 0 | 8 * x3o3o . o3o3o4x ♦ 64 | 96 128 | 64 192 96 | 16 128 144 32 | 0 32 96 48 4 | 0 24 32 6 | 0 8 4 | * 16
o3o3o4s o3o3o4x demi( . . . . ) . . . . | 128 | 6 4 | 12 24 6 | 4 4 48 36 16 | 1 16 16 72 24 1 | 4 24 24 48 6 | 6 16 16 12 | 4 4 4 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ . . o4s . . . . | 2 | 384 * | 4 4 0 | 2 2 16 6 0 | 1 8 8 24 16 0 | 4 12 12 16 1 | 6 8 8 4 | 4 2 2 demi( . . . . ) . . . x | 2 | * 256 | 0 6 3 | 0 0 12 18 3 | 0 4 4 36 18 1 | 1 12 12 36 4 | 3 12 12 12 | 3 4 4 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ sefa( . o3o4s ) . . . . | 3 | 3 0 | 512 * * | 1 1 4 0 0 | 1 4 4 6 0 0 | 4 6 6 4 0 | 6 4 4 1 | 4 1 1 . . o4s . . . x | 4 | 2 2 | * 768 * | 0 0 4 3 0 | 0 2 2 12 3 0 | 1 6 6 12 1 | 3 6 6 4 | 3 2 2 demi( . . . . ) . . o4x | 4 | 0 4 | * * 192 | 0 0 0 6 2 | 0 0 0 12 12 1 | 0 4 4 16 6 | 1 8 8 12 | 2 4 4 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ . o3o4s . . . . ♦ 4 | 6 0 | 4 0 0 | 128 * * * * | 1 4 0 0 0 0 | 4 6 0 0 0 | 6 4 0 0 | 4 1 0 sefa( o3o3o4s ) . . . . ♦ 4 | 6 0 | 4 0 0 | * 128 * * * | 1 0 4 0 0 0 | 4 0 6 0 0 | 6 0 4 0 | 4 0 1 sefa( . o3o4s ) . . . x ♦ 6 | 6 3 | 2 3 0 | * * 1024 * * | 0 0 2 3 0 0 | 1 3 3 3 0 | 3 3 3 1 | 3 1 1 . . o4s . . o4x ♦ 8 | 4 8 | 0 4 2 | * * * 576 * | 0 0 0 4 2 0 | 0 2 2 8 1 | 1 4 4 4 | 2 2 2 demi( . . . . ) . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * * 64 | 0 0 0 0 6 1 | 0 0 0 12 6 | 0 4 4 12 | 1 4 4 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ o3o3o4s . . . . ♦ 8 | 24 0 | 32 0 0 | 8 8 0 0 0 | 16 * * * * * ♦ 4 0 0 0 0 | 6 0 0 0 | 4 0 0 . o3o4s . . . x ♦ 8 | 12 4 | 8 6 0 | 2 0 4 0 0 | * 256 * * * * | 1 3 0 0 0 | 3 3 0 0 | 3 1 0 sefa( o3o3o4s ) . . . x ♦ 8 | 12 4 | 8 6 0 | 0 2 4 0 0 | * * 256 * * * | 1 0 3 0 0 | 3 0 3 0 | 3 0 1 sefa( . o3o4s ) . . o4x ♦ 12 | 12 12 | 4 12 3 | 0 0 4 3 0 | * * * 768 * * | 0 1 1 2 0 | 1 2 2 1 | 2 1 1 . . o4s . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 0 0 6 2 | * * * * 192 * | 0 0 0 4 1 | 0 2 2 4 | 1 2 2 demi( . . . . ) o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 0 0 8 | * * * * * 8 ♦ 0 0 0 0 6 | 0 0 0 12 | 0 4 4 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ o3o3o4s . . . x ♦ 16 | 48 8 | 64 24 0 | 16 16 32 0 0 | 2 8 8 0 0 0 | 32 * * * * | 3 0 0 0 | 3 0 0 . o3o4s . . o4x ♦ 16 | 24 16 | 16 24 4 | 4 0 16 6 0 | 0 4 0 4 0 0 | * 192 * * * | 1 2 0 0 | 2 1 0 sefa( o3o3o4s ) . . o4x ♦ 16 | 24 16 | 16 24 4 | 0 4 16 6 0 | 0 0 4 4 0 0 | * * 192 * * | 1 0 2 0 | 2 0 1 sefa( . o3o4s ) . o3o4x ♦ 24 | 24 36 | 8 36 18 | 0 0 12 18 3 | 0 0 0 6 3 0 | * * * 256 * | 0 1 1 1 | 1 1 1 . . o4s o3o3o4x ♦ 32 | 16 64 | 0 32 48 | 0 0 0 24 16 | 0 0 0 0 8 2 | * * * * 24 | 0 0 0 4 | 0 2 2 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ o3o3o4s . . o4x ♦ 32 | 96 32 | 128 96 8 | 32 32 128 24 0 | 4 32 32 32 0 0 | 4 8 8 0 0 | 24 * * * | 2 0 0 . o3o4s . o3o4x ♦ 32 | 48 48 | 32 72 24 | 8 0 48 36 4 | 0 12 0 24 6 0 | 0 6 0 4 0 | * 64 * * | 1 1 0 sefa( o3o3o4s ) . o3o4x ♦ 32 | 48 48 | 32 72 24 | 0 8 48 36 4 | 0 0 12 24 6 0 | 0 0 6 4 0 | * * 64 * | 1 0 1 sefa( . o3o4s ) o3o3o4x ♦ 48 | 48 96 | 16 96 72 | 0 0 32 72 24 | 0 0 0 24 24 3 | 0 0 0 8 3 | * * * 32 | 0 1 1 ------------------------+-----+---------+-------------+---------------------+----------------------+-------------------+-------------+------ o3o3o4s . o3o4x ♦ 64 | 192 96 | 256 288 48 | 64 64 384 144 8 | 8 96 96 192 24 0 | 12 48 48 32 0 | 6 8 8 0 | 8 * * . o3o4s o3o3o4x ♦ 64 | 96 128 | 64 192 96 | 16 0 128 144 32 | 0 32 0 96 48 4 | 0 24 0 32 6 | 0 8 0 4 | * 8 * sefa( o3o3o4s ) o3o3o4x ♦ 64 | 96 128 | 64 192 96 | 0 16 128 144 32 | 0 0 32 96 48 4 | 0 0 24 32 6 | 0 0 8 4 | * * 8 starting figure: o3o3o4x o3o3o4x
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