| Acronym | octhex |
| Name |
octahedron - hexadecachoron duoprism, vertex figure of troch |
| Circumradius | 1 |
| Volume | sqrt(2)/18 = 0.078567 |
| Face vector | 48, 240, 544, 680, 478, 172, 24 |
| Confer |
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Incidence matrix according to Dynkin symbol
x3o4o x3o3o4o o3o4o o3o3o4o | 48 | 4 6 | 4 24 12 | 1 24 48 8 | 6 48 32 1 | 12 32 4 | 8 4 --------------+----+--------+------------+--------------+--------------+-----------+----- x . . . . . . | 2 | 96 * | 2 6 0 | 1 12 12 0 | 6 24 8 0 | 12 16 1 | 8 2 . . . x . . . | 2 | * 144 | 0 4 4 | 0 4 16 4 | 1 16 16 1 | 4 16 4 | 4 4 --------------+----+--------+------------+--------------+--------------+-----------+----- x3o . . . . . | 3 | 3 0 | 64 * * | 1 6 0 0 | 6 12 0 0 | 12 8 0 | 8 1 x . . x . . . | 4 | 2 2 | * 288 * | 0 2 4 0 | 1 8 4 0 | 4 8 1 | 4 2 . . . x3o . . | 3 | 0 3 | * * 192 | 0 0 4 2 | 0 4 8 1 | 1 8 4 | 2 4 --------------+----+--------+------------+--------------+--------------+-----------+----- x3o4o . . . . ♦ 6 | 12 0 | 8 0 0 | 8 * * * ♦ 6 0 0 0 | 12 0 0 | 8 0 x3o . x . . . ♦ 6 | 6 3 | 2 3 0 | * 192 * * | 1 4 0 0 | 4 4 0 | 4 1 x . . x3o . . ♦ 6 | 3 6 | 0 3 2 | * * 384 * | 0 2 2 0 | 1 4 1 | 2 2 . . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * * 96 | 0 0 4 1 | 0 4 4 | 1 4 --------------+----+--------+------------+--------------+--------------+-----------+----- x3o4o x . . . ♦ 12 | 24 6 | 16 12 0 | 2 8 0 0 | 24 * * * | 4 0 0 | 4 0 x3o . x3o . . ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 | * 256 * * | 1 2 0 | 2 1 x . . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 | * * 192 * | 0 2 1 | 1 2 . . . x3o3o4o ♦ 8 | 0 24 | 0 0 32 | 0 0 0 16 | * * * 6 | 0 0 4 | 0 4 --------------+----+--------+------------+--------------+--------------+-----------+----- x3o4o x3o . . ♦ 18 | 36 18 | 24 36 6 | 3 24 12 0 | 3 8 0 0 | 32 * * | 2 0 x3o . x3o3o . ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 | 0 4 3 0 | * 128 * | 1 1 x . . x3o3o4o ♦ 16 | 8 48 | 0 24 64 | 0 0 32 32 | 0 0 16 2 | * * 12 | 0 2 --------------+----+--------+------------+--------------+--------------+-----------+----- x3o4o x3o3o . ♦ 24 | 48 48 | 32 72 24 | 4 48 48 6 | 6 32 12 0 | 4 8 0 | 16 * x3o . x3o3o4o ♦ 24 | 24 72 | 8 72 96 | 0 24 96 48 | 0 32 48 3 | 0 16 3 | * 8
o3x3o x3o3o4o o3o3o o3o3o4o | 48 | 4 6 | 2 2 24 12 | 1 12 12 48 8 | 6 24 24 32 1 | 12 16 16 4 | 8 2 2 --------------+----+--------+---------------+----------------+------------------+-------------+------- . x . . . . . | 2 | 96 * | 1 1 6 0 | 1 6 6 12 0 | 6 12 12 8 0 | 12 8 8 1 | 8 1 1 . . . x . . . | 2 | * 144 | 0 0 4 4 | 0 2 2 16 4 | 1 8 8 16 1 | 4 8 8 4 | 4 2 2 --------------+----+--------+---------------+----------------+------------------+-------------+------- o3x . . . . . | 3 | 3 0 | 32 * * * | 1 6 0 0 0 | 6 12 0 0 0 | 12 8 0 0 | 8 1 0 . x3o . . . . | 3 | 3 0 | * 32 * * | 1 0 6 0 0 | 6 0 12 0 0 | 12 0 8 0 | 8 0 1 . x . x . . . | 4 | 2 2 | * * 288 * | 0 1 1 4 0 | 1 4 4 4 0 | 4 4 4 1 | 4 1 1 . . . x3o . . | 3 | 0 3 | * * * 192 | 0 0 0 4 2 | 0 2 2 8 1 | 1 4 4 4 | 2 2 2 --------------+----+--------+---------------+----------------+------------------+-------------+------- o3x3o . . . . ♦ 6 | 12 0 | 4 4 0 0 | 8 * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 8 0 0 o3x . x . . . ♦ 6 | 6 3 | 2 0 3 0 | * 96 * * * | 1 4 0 0 0 | 4 4 0 0 | 4 1 0 . x3o x . . . ♦ 6 | 6 3 | 0 2 3 0 | * * 96 * * | 1 0 4 0 0 | 4 0 4 0 | 4 0 1 . x . x3o . . ♦ 6 | 3 6 | 0 0 3 2 | * * * 384 * | 0 1 1 2 0 | 1 2 2 1 | 2 1 1 . . . x3o3o . ♦ 4 | 0 6 | 0 0 0 4 | * * * * 96 | 0 0 0 4 1 | 0 2 2 4 | 1 2 2 --------------+----+--------+---------------+----------------+------------------+-------------+------- o3x3o x . . . ♦ 12 | 24 6 | 8 8 12 0 | 2 4 4 0 0 | 24 * * * * | 4 0 0 0 | 4 0 0 o3x . x3o . . ♦ 9 | 9 9 | 3 0 9 3 | 0 3 0 3 0 | * 128 * * * | 1 2 0 0 | 2 1 0 . x3o x3o . . ♦ 9 | 9 9 | 0 3 9 3 | 0 0 3 3 0 | * * 128 * * | 1 0 2 0 | 2 0 1 . x . x3o3o . ♦ 8 | 4 12 | 0 0 6 8 | 0 0 0 4 2 | * * * 192 * | 0 1 1 1 | 1 1 1 . . . x3o3o4o ♦ 8 | 0 24 | 0 0 0 32 | 0 0 0 0 16 | * * * * 6 | 0 0 0 4 | 0 2 2 --------------+----+--------+---------------+----------------+------------------+-------------+------- o3x3o x3o . . ♦ 18 | 36 18 | 12 12 36 6 | 3 12 12 12 0 | 3 4 4 0 0 | 32 * * * | 2 0 0 o3x . x3o3o . ♦ 12 | 12 18 | 4 0 18 12 | 0 6 0 12 3 | 0 4 0 3 0 | * 64 * * | 1 1 0 . x3o x3o3o . ♦ 12 | 12 18 | 0 4 18 12 | 0 0 6 12 3 | 0 0 4 3 0 | * * 64 * | 1 0 1 . x . x3o3o4o ♦ 16 | 8 48 | 0 0 24 64 | 0 0 0 32 32 | 0 0 0 16 2 | * * * 12 | 0 1 1 --------------+----+--------+---------------+----------------+------------------+-------------+------- o3x3o x3o3o . ♦ 24 | 48 48 | 16 16 72 24 | 4 24 24 48 6 | 6 16 16 12 0 | 4 4 4 0 | 16 * * o3x . x3o3o4o ♦ 24 | 24 72 | 8 0 72 96 | 0 24 0 96 48 | 0 32 0 48 3 | 0 16 0 3 | * 4 * . x3o x3o3o4o ♦ 24 | 24 72 | 0 8 72 96 | 0 0 24 96 48 | 0 0 32 48 3 | 0 0 16 3 | * * 4
x3o4o x3o3o *e3o o3o4o o3o3o *e3o | 48 | 4 6 | 4 24 12 | 1 24 48 4 4 | 6 48 16 16 1 | 12 16 16 4 | 4 4 4 -----------------+----+--------+------------+-----------------+----------------+-------------+------ x . . . . . . | 2 | 96 * | 2 6 0 | 1 12 12 0 0 | 6 24 4 4 0 | 12 8 8 1 | 4 4 2 . . . x . . . | 2 | * 144 | 0 4 4 | 0 4 16 2 2 | 1 16 8 8 1 | 4 8 8 4 | 2 2 4 -----------------+----+--------+------------+-----------------+----------------+-------------+------ x3o . . . . . | 3 | 3 0 | 64 * * | 1 6 0 0 0 | 6 12 0 0 0 | 12 4 4 0 | 4 4 1 x . . x . . . | 4 | 2 2 | * 288 * | 0 2 4 0 0 | 1 8 2 2 0 | 4 4 4 1 | 2 2 2 . . . x3o . . | 3 | 0 3 | * * 192 | 0 0 4 1 1 | 0 4 4 4 1 | 1 4 4 4 | 1 1 4 -----------------+----+--------+------------+-----------------+----------------+-------------+------ x3o4o . . . . ♦ 6 | 12 0 | 8 0 0 | 8 * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 x3o . x . . . ♦ 6 | 6 3 | 2 3 0 | * 192 * * * | 1 4 0 0 0 | 4 2 2 0 | 2 2 1 x . . x3o . . ♦ 6 | 3 6 | 0 3 2 | * * 384 * * | 0 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * * 48 * | 0 0 4 0 1 | 0 4 0 4 | 1 0 4 . . . x3o . *e3o ♦ 4 | 0 6 | 0 0 4 | * * * * 48 | 0 0 0 4 1 | 0 0 4 4 | 0 1 4 -----------------+----+--------+------------+-----------------+----------------+-------------+------ x3o4o x . . . ♦ 12 | 24 6 | 16 12 0 | 2 8 0 0 0 | 24 * * * * | 4 0 0 0 | 2 2 0 x3o . x3o . . ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 0 | * 256 * * * | 1 1 1 0 | 1 1 1 x . . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 0 | * * 96 * * | 0 2 0 1 | 1 0 2 x . . x3o . *e3o ♦ 8 | 4 12 | 0 6 8 | 0 0 4 0 2 | * * * 96 * | 0 0 2 1 | 0 1 2 . . . x3o3o *e3o ♦ 8 | 0 24 | 0 0 32 | 0 0 0 8 8 | * * * * 6 | 0 0 0 4 | 0 0 4 -----------------+----+--------+------------+-----------------+----------------+-------------+------ x3o4o x3o . . ♦ 18 | 36 18 | 24 36 6 | 3 24 12 0 0 | 3 8 0 0 0 | 32 * * * | 1 1 0 x3o . x3o3o . ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 0 | 0 4 3 0 0 | * 64 * * | 1 0 1 x3o . x3o . *e3o ♦ 12 | 12 18 | 4 18 12 | 0 6 12 0 3 | 0 4 0 3 0 | * * 64 * | 0 1 1 x . . x3o3o *e3o ♦ 16 | 8 48 | 0 24 64 | 0 0 32 16 16 | 0 0 8 8 2 | * * * 12 | 0 0 2 -----------------+----+--------+------------+-----------------+----------------+-------------+------ x3o4o x3o3o . ♦ 24 | 48 48 | 32 72 24 | 4 48 48 6 0 | 6 32 12 0 0 | 4 8 0 0 | 8 * * x3o4o x3o . *e3o ♦ 24 | 48 48 | 32 72 24 | 4 48 48 0 6 | 6 32 0 12 0 | 4 0 8 0 | * 8 * x3o . x3o3o *e3o ♦ 24 | 24 72 | 8 72 96 | 0 24 96 24 24 | 0 32 24 24 3 | 0 8 8 3 | * * 8
o3x3o x3o3o *e3o o3o3o o3o3o *e3o | 48 | 4 6 | 2 2 24 12 | 1 12 12 48 4 4 | 6 24 24 16 16 1 | 12 8 8 8 8 4 | 4 4 2 2 -----------------+----+--------+---------------+-------------------+--------------------+-------------------+-------- . x . . . . . | 2 | 96 * | 1 1 6 0 | 1 6 6 12 0 0 | 6 12 12 4 4 0 | 12 4 4 4 4 1 | 4 4 1 1 . . . x . . . | 2 | * 144 | 0 0 4 4 | 0 2 2 16 2 2 | 1 8 8 8 8 1 | 4 4 4 4 4 4 | 2 2 2 2 -----------------+----+--------+---------------+-------------------+--------------------+-------------------+-------- o3x . . . . . | 3 | 3 0 | 32 * * * | 1 6 0 0 0 0 | 6 12 0 0 0 0 | 12 4 4 0 0 0 | 4 4 1 0 . x3o . . . . | 3 | 3 0 | * 32 * * | 1 0 6 0 0 0 | 6 0 12 0 0 0 | 12 0 0 4 4 0 | 4 4 0 1 . x . x . . . | 4 | 2 2 | * * 288 * | 0 1 1 4 0 0 | 1 4 4 2 2 0 | 4 2 2 2 2 1 | 2 2 1 1 . . . x3o . . | 3 | 0 3 | * * * 192 | 0 0 0 4 1 1 | 0 2 2 4 4 1 | 1 2 2 2 2 4 | 1 1 2 2 -----------------+----+--------+---------------+-------------------+--------------------+-------------------+-------- o3x3o . . . . ♦ 6 | 12 0 | 4 4 0 0 | 8 * * * * * ♦ 6 0 0 0 0 0 | 12 0 0 0 0 0 | 4 4 0 0 o3x . x . . . ♦ 6 | 6 3 | 2 0 3 0 | * 96 * * * * | 1 4 0 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0 . x3o x . . . ♦ 6 | 6 3 | 0 2 3 0 | * * 96 * * * | 1 0 4 0 0 0 | 4 0 0 2 2 0 | 2 2 0 1 . x . x3o . . ♦ 6 | 3 6 | 0 0 3 2 | * * * 384 * * | 0 1 1 1 1 0 | 1 1 1 1 1 1 | 1 1 1 1 . . . x3o3o . ♦ 4 | 0 6 | 0 0 0 4 | * * * * 48 * | 0 0 0 4 0 1 | 0 2 0 2 0 4 | 1 0 2 2 . . . x3o . *e3o ♦ 4 | 0 6 | 0 0 0 4 | * * * * * 48 | 0 0 0 0 4 1 | 0 0 2 0 2 4 | 0 1 2 2 -----------------+----+--------+---------------+-------------------+--------------------+-------------------+-------- o3x3o x . . . ♦ 12 | 24 6 | 8 8 12 0 | 2 4 4 0 0 0 | 24 * * * * * | 4 0 0 0 0 0 | 2 2 0 0 o3x . x3o . . ♦ 9 | 9 9 | 3 0 9 3 | 0 3 0 3 0 0 | * 128 * * * * | 1 1 1 0 0 0 | 1 1 1 0 . x3o x3o . . ♦ 9 | 9 9 | 0 3 9 3 | 0 0 3 3 0 0 | * * 128 * * * | 1 0 0 1 1 0 | 1 1 0 1 . x . x3o3o . ♦ 8 | 4 12 | 0 0 6 8 | 0 0 0 4 2 0 | * * * 96 * * | 0 1 0 1 0 1 | 1 0 1 1 . x . x3o . *e3o ♦ 8 | 4 12 | 0 0 6 8 | 0 0 0 4 0 2 | * * * * 96 * | 0 0 1 0 1 1 | 0 1 1 1 . . . x3o3o *e3o ♦ 8 | 0 24 | 0 0 0 32 | 0 0 0 0 8 8 | * * * * * 6 | 0 0 0 0 0 4 | 0 0 2 2 -----------------+----+--------+---------------+-------------------+--------------------+-------------------+-------- o3x3o x3o . . ♦ 18 | 36 18 | 12 12 36 6 | 3 12 12 12 0 0 | 3 4 4 0 0 0 | 32 * * * * * | 1 1 0 0 o3x . x3o3o . ♦ 12 | 12 18 | 4 0 18 12 | 0 6 0 12 3 0 | 0 4 0 3 0 0 | * 32 * * * * | 1 0 1 0 o3x . x3o . *e3o ♦ 12 | 12 18 | 4 0 18 12 | 0 6 0 12 0 3 | 0 4 0 0 3 0 | * * 32 * * * | 0 1 1 0 . x3o x3o3o . ♦ 12 | 12 18 | 0 4 18 12 | 0 0 6 12 3 0 | 0 0 4 3 0 0 | * * * 32 * * | 1 0 0 1 . x3o x3o . *e3o ♦ 12 | 12 18 | 0 4 18 12 | 0 0 6 12 0 3 | 0 0 4 0 3 0 | * * * * 32 * | 0 1 0 1 . x . x3o3o *e3o ♦ 16 | 8 48 | 0 0 24 64 | 0 0 0 32 16 16 | 0 0 0 8 8 2 | * * * * * 12 | 0 0 1 1 -----------------+----+--------+---------------+-------------------+--------------------+-------------------+-------- o3x3o x3o3o . ♦ 24 | 48 48 | 16 16 72 24 | 4 24 24 48 6 0 | 6 16 16 12 0 0 | 4 4 0 4 0 0 | 8 * * * o3x3o x3o . *e3o ♦ 24 | 48 48 | 16 16 72 24 | 4 24 24 48 0 6 | 6 16 16 0 12 0 | 4 0 4 0 4 0 | * 8 * * o3x . x3o3o *e3o ♦ 24 | 24 72 | 8 0 72 96 | 0 24 0 96 24 24 | 0 32 0 24 24 3 | 0 8 8 0 0 3 | * * 4 * . x3o x3o3o *e3o ♦ 24 | 24 72 | 0 8 72 96 | 0 0 24 96 24 24 | 0 0 32 24 24 3 | 0 0 0 8 8 3 | * * * 4
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