| Acronym | corap |
| Name | cuboctahedron - rectified-pentachoron duoprism |
| Circumradius | sqrt(8/5) = 1.264911 |
| Volume | 55 sqrt(10)/288 = 0.603907 |
| Face vector | 120, 600, 1220, 1270, 702, 194, 24 |
| Confer |
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Incidence matrix according to Dynkin symbol
o3x4o o3x3o3o . . . . . . . | 120 | 4 6 | 2 2 24 3 6 | 1 12 12 12 24 3 2 | 6 6 12 6 12 12 8 1 | 3 6 6 4 6 4 4 | 3 2 2 2 --------------+-----+---------+-------------------+--------------------------+-----------------------------+----------------------+-------- . x . . . . . | 2 | 240 * | 1 1 6 0 0 | 1 6 6 3 6 0 0 | 6 3 6 3 6 3 2 0 | 3 6 3 2 3 2 1 | 3 2 1 1 . . . . x . . | 2 | * 360 | 0 0 4 1 2 | 0 2 2 4 8 2 1 | 1 2 4 2 4 8 4 1 | 1 2 4 2 4 2 4 | 2 1 2 2 --------------+-----+---------+-------------------+--------------------------+-----------------------------+----------------------+-------- o3x . . . . . | 3 | 3 0 | 80 * * * * | 1 6 0 0 0 0 0 | 6 3 6 0 0 0 0 0 | 3 6 3 2 0 0 0 | 3 2 1 0 . x4o . . . . | 4 | 4 0 | * 60 * * * | 1 0 6 0 0 0 0 | 6 0 0 3 6 0 0 0 | 3 6 0 0 3 2 0 | 3 2 0 1 . x . . x . . | 4 | 2 2 | * * 720 * * | 0 1 1 1 2 0 0 | 1 1 2 1 2 2 1 0 | 1 2 2 1 2 1 1 | 2 1 1 1 . . . o3x . . | 3 | 0 3 | * * * 120 * | 0 0 0 4 0 2 0 | 0 2 0 2 0 8 0 1 | 1 0 4 0 4 0 4 | 2 0 2 2 . . . . x3o . | 3 | 0 3 | * * * * 240 | 0 0 0 0 4 1 1 | 0 0 2 0 2 4 4 1 | 0 1 2 2 2 2 4 | 1 1 2 2 --------------+-----+---------+-------------------+--------------------------+-----------------------------+----------------------+-------- o3x4o . . . . ♦ 12 | 24 0 | 8 6 0 0 0 | 10 * * * * * * ♦ 6 0 0 0 0 0 0 0 | 3 6 0 0 0 0 0 | 3 2 0 0 o3x . . x . . ♦ 6 | 6 3 | 2 0 3 0 0 | * 240 * * * * * | 1 1 2 0 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x4o . x . . ♦ 8 | 8 4 | 0 2 4 0 0 | * * 180 * * * * | 1 0 0 1 2 0 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . x . o3x . . ♦ 6 | 3 6 | 0 0 3 2 0 | * * * 240 * * * | 0 1 0 1 0 2 0 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . x . . x3o . ♦ 6 | 3 6 | 0 0 3 0 2 | * * * * 480 * * | 0 0 1 0 1 1 1 0 | 0 1 1 1 1 1 1 | 1 1 1 1 . . . o3x3o . ♦ 6 | 0 12 | 0 0 0 4 4 | * * * * * 60 * | 0 0 0 0 0 4 0 1 | 0 0 2 0 2 0 4 | 1 0 2 2 . . . . x3o3o ♦ 4 | 0 6 | 0 0 0 0 4 | * * * * * * 60 | 0 0 0 0 0 0 4 1 | 0 0 0 2 0 2 4 | 0 1 2 2 --------------+-----+---------+-------------------+--------------------------+-----------------------------+----------------------+-------- o3x4o . x . . ♦ 24 | 48 12 | 16 12 24 0 0 | 2 8 6 0 0 0 0 | 30 * * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 o3x . o3x . . ♦ 9 | 9 9 | 3 0 9 3 0 | 0 3 0 3 0 0 0 | * 80 * * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 o3x . . x3o . ♦ 9 | 9 9 | 3 0 9 0 3 | 0 3 0 0 3 0 0 | * * 160 * * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x4o o3x . . ♦ 12 | 12 12 | 0 3 12 4 0 | 0 0 3 4 0 0 0 | * * * 60 * * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x4o . x3o . ♦ 12 | 12 12 | 0 3 12 0 4 | 0 0 3 0 4 0 0 | * * * * 120 * * * | 0 1 0 0 1 1 0 | 1 1 0 1 . x . o3x3o . ♦ 12 | 6 24 | 0 0 12 8 8 | 0 0 0 4 4 2 0 | * * * * * 120 * * | 0 0 1 0 1 0 1 | 1 0 1 1 . x . . x3o3o ♦ 8 | 4 12 | 0 0 6 0 8 | 0 0 0 0 4 0 2 | * * * * * * 120 * | 0 0 0 1 0 1 1 | 0 1 1 1 . . . o3x3o3o ♦ 10 | 0 30 | 0 0 0 10 20 | 0 0 0 0 0 5 5 | * * * * * * * 12 | 0 0 0 0 0 0 4 | 0 0 2 2 --------------+-----+---------+-------------------+--------------------------+-----------------------------+----------------------+-------- o3x4o o3x . . ♦ 36 | 72 36 | 24 18 72 12 0 | 3 24 18 24 0 0 0 | 3 8 0 6 0 0 0 0 | 10 * * * * * * | 2 0 0 0 o3x4o . x3o . ♦ 36 | 72 36 | 24 18 72 0 12 | 3 24 18 0 24 0 0 | 3 0 8 0 6 0 0 0 | * 20 * * * * * | 1 1 0 0 o3x . o3x3o . ♦ 18 | 18 36 | 6 0 36 12 12 | 0 12 0 12 12 3 0 | 0 4 4 0 0 3 0 0 | * * 40 * * * * | 1 0 1 0 o3x . . x3o3o ♦ 12 | 12 18 | 4 0 18 0 12 | 0 6 0 0 12 0 3 | 0 0 4 0 0 0 3 0 | * * * 40 * * * | 0 1 1 0 . x4o o3x3o . ♦ 24 | 24 48 | 0 6 48 16 16 | 0 0 12 16 16 4 0 | 0 0 0 4 4 4 0 0 | * * * * 30 * * | 1 0 0 1 . x4o . x3o3o ♦ 16 | 16 24 | 0 4 24 0 16 | 0 0 6 0 16 0 4 | 0 0 0 0 4 0 4 0 | * * * * * 30 * | 0 1 0 1 . x . o3x3o3o ♦ 20 | 10 60 | 0 0 30 20 40 | 0 0 0 10 20 10 10 | 0 0 0 0 0 5 5 2 | * * * * * * 24 | 0 0 1 1 --------------+-----+---------+-------------------+--------------------------+-----------------------------+----------------------+-------- o3x4o o3x3o . ♦ 72 | 144 144 | 48 36 288 48 48 | 6 96 72 96 96 12 0 | 12 32 32 24 24 24 0 0 | 4 4 8 0 6 0 0 | 5 * * * o3x4o . x3o3o ♦ 48 | 96 72 | 32 24 144 0 48 | 4 48 36 0 96 0 12 | 6 0 32 0 24 0 24 0 | 0 4 0 8 0 6 0 | * 5 * * o3x . o3x3o3o ♦ 30 | 30 90 | 10 0 90 30 60 | 0 30 0 30 60 15 15 | 0 10 20 0 0 15 15 3 | 0 0 5 5 0 0 3 | * * 8 * . x4o o3x3o3o ♦ 40 | 40 120 | 0 10 120 40 80 | 0 0 30 40 80 20 20 | 0 0 0 10 20 20 20 4 | 0 0 0 0 5 5 4 | * * * 6
x3o3x o3x3o3o . . . . . . . | 120 | 2 2 6 | 1 2 12 1 12 3 6 | 1 6 12 6 12 6 6 12 3 2 | 6 3 6 6 12 6 4 3 6 6 4 1 | 3 6 3 2 6 4 2 3 2 2 | 3 2 1 2 1 --------------+-----+-------------+--------------------------+--------------------------------------+--------------------------------------+-------------------------------+---------- x . . . . . . | 2 | 120 * * | 1 1 6 0 0 0 0 | 1 6 6 3 6 0 0 0 0 0 | 6 3 6 3 6 3 2 0 0 0 0 0 | 3 6 3 2 3 2 1 0 0 0 | 3 2 1 1 0 . . x . . . . | 2 | * 120 * | 0 1 0 1 6 0 0 | 1 0 6 0 0 6 3 6 0 0 | 6 0 0 3 6 0 0 3 6 3 2 0 | 3 6 0 0 3 2 0 3 2 1 | 3 2 0 1 1 . . . . x . . | 2 | * * 360 | 0 0 2 0 2 1 2 | 0 1 2 2 4 1 2 4 2 1 | 1 1 2 2 4 4 2 1 2 4 2 1 | 1 2 2 1 4 2 2 2 1 2 | 2 1 1 2 1 --------------+-----+-------------+--------------------------+--------------------------------------+--------------------------------------+-------------------------------+---------- x3o . . . . . | 3 | 3 0 0 | 40 * * * * * * | 1 6 0 0 0 0 0 0 0 0 | 6 3 6 0 0 0 0 0 0 0 0 0 | 3 6 3 2 0 0 0 0 0 0 | 3 2 1 0 0 x . x . . . . | 4 | 2 2 0 | * 60 * * * * * | 1 0 6 0 0 0 0 0 0 0 | 6 0 0 3 6 0 0 0 0 0 0 0 | 3 6 0 0 3 2 0 0 0 0 | 3 2 0 1 0 x . . . x . . | 4 | 2 0 2 | * * 360 * * * * | 0 1 1 1 2 0 0 0 0 0 | 1 1 2 1 2 2 1 0 0 0 0 0 | 1 2 2 1 2 1 1 0 0 0 | 2 1 1 1 0 . o3x . . . . | 3 | 0 3 0 | * * * 40 * * * | 1 0 0 0 0 6 0 0 0 0 | 6 0 0 0 0 0 0 3 6 0 0 0 | 3 6 0 0 0 0 0 3 2 0 | 3 2 0 0 1 . . x . x . . | 4 | 0 2 2 | * * * * 360 * * | 0 0 1 0 0 1 1 2 0 0 | 1 0 0 1 2 0 0 1 2 2 1 0 | 1 2 0 0 2 1 0 2 1 1 | 2 1 0 1 1 . . . o3x . . | 3 | 0 0 3 | * * * * * 120 * | 0 0 0 2 0 0 2 0 2 0 | 0 1 0 2 0 4 0 1 0 4 0 1 | 1 0 2 0 4 0 2 2 0 2 | 2 0 1 2 1 . . . . x3o . | 3 | 0 0 3 | * * * * * * 240 | 0 0 0 0 2 0 0 2 1 1 | 0 0 1 0 2 2 2 0 1 2 2 1 | 0 1 1 1 2 2 2 1 1 2 | 1 1 1 2 1 --------------+-----+-------------+--------------------------+--------------------------------------+--------------------------------------+-------------------------------+---------- x3o3x . . . . ♦ 12 | 12 12 0 | 4 6 0 4 0 0 0 | 10 * * * * * * * * * ♦ 6 0 0 0 0 0 0 0 0 0 0 0 | 3 6 0 0 0 0 0 0 0 0 | 3 2 0 0 0 x3o . . x . . ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 120 * * * * * * * * | 1 1 2 0 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 0 | 2 1 1 0 0 x . x . x . . ♦ 8 | 4 4 4 | 0 2 2 0 2 0 0 | * * 180 * * * * * * * | 1 0 0 1 2 0 0 0 0 0 0 0 | 1 2 0 0 2 1 0 0 0 0 | 2 1 0 1 0 x . . o3x . . ♦ 6 | 3 0 6 | 0 0 3 0 0 2 0 | * * * 120 * * * * * * | 0 1 0 1 0 2 0 0 0 0 0 0 | 1 0 2 0 2 0 1 0 0 0 | 2 0 1 1 0 x . . . x3o . ♦ 6 | 3 0 6 | 0 0 3 0 0 0 2 | * * * * 240 * * * * * | 0 0 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0 . o3x . x . . ♦ 6 | 0 6 3 | 0 0 0 2 3 0 0 | * * * * * 120 * * * * | 1 0 0 0 0 0 0 1 2 0 0 0 | 1 2 0 0 0 0 0 2 1 0 | 2 1 0 0 1 . . x o3x . . ♦ 6 | 0 3 6 | 0 0 0 0 3 2 0 | * * * * * * 120 * * * | 0 0 0 1 0 0 0 1 0 2 0 0 | 1 0 0 0 2 0 0 2 0 1 | 2 0 0 1 1 . . x . x3o . ♦ 6 | 0 3 6 | 0 0 0 0 3 0 2 | * * * * * * * 240 * * | 0 0 0 0 1 0 0 0 1 1 1 0 | 0 1 0 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . o3x3o . ♦ 6 | 0 0 12 | 0 0 0 0 0 4 4 | * * * * * * * * 60 * | 0 0 0 0 0 2 0 0 0 2 0 1 | 0 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x3o3o ♦ 4 | 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * * * 60 | 0 0 0 0 0 0 2 0 0 0 2 1 | 0 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 --------------+-----+-------------+--------------------------+--------------------------------------+--------------------------------------+-------------------------------+---------- x3o3x . x . . ♦ 24 | 24 24 12 | 8 12 12 8 12 0 0 | 2 4 6 0 0 4 0 0 0 0 | 30 * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 | 2 1 0 0 0 x3o . o3x . . ♦ 9 | 9 0 9 | 3 0 9 0 0 3 0 | 0 3 0 3 0 0 0 0 0 0 | * 40 * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 | 2 0 1 0 0 x3o . . x3o . ♦ 9 | 9 0 9 | 3 0 9 0 0 0 3 | 0 3 0 0 3 0 0 0 0 0 | * * 80 * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . x o3x . . ♦ 12 | 6 6 12 | 0 3 6 0 6 4 0 | 0 0 3 2 0 0 2 0 0 0 | * * * 60 * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 | 2 0 0 1 0 x . x . x3o . ♦ 12 | 6 6 12 | 0 3 6 0 6 0 4 | 0 0 3 0 2 0 0 2 0 0 | * * * * 120 * * * * * * * | 0 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . o3x3o . ♦ 12 | 6 0 24 | 0 0 12 0 0 8 8 | 0 0 0 4 4 0 0 0 2 0 | * * * * * 60 * * * * * * | 0 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x3o3o ♦ 8 | 4 0 12 | 0 0 6 0 0 0 8 | 0 0 0 0 4 0 0 0 0 2 | * * * * * * 60 * * * * * | 0 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3x o3x . . ♦ 9 | 0 9 9 | 0 0 0 3 9 3 0 | 0 0 0 0 0 3 3 0 0 0 | * * * * * * * 40 * * * * | 1 0 0 0 0 0 0 2 0 0 | 2 0 0 0 1 . o3x . x3o . ♦ 9 | 0 9 9 | 0 0 0 3 9 0 3 | 0 0 0 0 0 3 0 3 0 0 | * * * * * * * * 80 * * * | 0 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x o3x3o . ♦ 12 | 0 6 24 | 0 0 0 0 12 8 8 | 0 0 0 0 0 0 4 4 2 0 | * * * * * * * * * 60 * * | 0 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x3o3o ♦ 8 | 0 4 12 | 0 0 0 0 6 0 8 | 0 0 0 0 0 0 0 4 0 2 | * * * * * * * * * * 60 * | 0 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . o3x3o3o ♦ 10 | 0 0 30 | 0 0 0 0 0 10 20 | 0 0 0 0 0 0 0 0 5 5 | * * * * * * * * * * * 12 | 0 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 --------------+-----+-------------+--------------------------+--------------------------------------+--------------------------------------+-------------------------------+---------- x3o3x o3x . . ♦ 36 | 36 36 36 | 12 18 36 12 36 12 0 | 3 12 18 12 0 12 12 0 0 0 | 3 4 0 6 0 0 0 4 0 0 0 0 | 10 * * * * * * * * * | 2 0 0 0 0 x3o3x . x3o . ♦ 36 | 36 36 36 | 12 18 36 12 36 0 12 | 3 12 18 0 12 12 0 12 0 0 | 3 0 4 0 6 0 0 0 4 0 0 0 | * 20 * * * * * * * * | 1 1 0 0 0 x3o . o3x3o . ♦ 18 | 18 0 36 | 6 0 36 0 0 12 12 | 0 12 0 12 12 0 0 0 3 0 | 0 4 4 0 0 3 0 0 0 0 0 0 | * * 20 * * * * * * * | 1 0 1 0 0 x3o . . x3o3o ♦ 12 | 12 0 18 | 4 0 18 0 0 0 12 | 0 6 0 0 12 0 0 0 0 3 | 0 0 4 0 0 0 3 0 0 0 0 0 | * * * 20 * * * * * * | 0 1 1 0 0 x . x o3x3o . ♦ 24 | 12 12 48 | 0 6 24 0 24 16 16 | 0 0 12 8 8 0 8 8 4 0 | 0 0 0 4 4 2 0 0 0 2 0 0 | * * * * 30 * * * * * | 1 0 0 1 0 x . x . x3o3o ♦ 16 | 8 8 24 | 0 4 12 0 12 0 16 | 0 0 6 0 8 0 0 8 0 4 | 0 0 0 0 4 0 2 0 0 0 2 0 | * * * * * 30 * * * * | 0 1 0 1 0 x . . o3x3o3o ♦ 20 | 10 0 60 | 0 0 30 0 0 20 40 | 0 0 0 10 20 0 0 0 10 10 | 0 0 0 0 0 5 5 0 0 0 0 2 | * * * * * * 12 * * * | 0 0 1 1 0 . o3x o3x3o . ♦ 18 | 0 18 36 | 0 0 0 6 36 12 12 | 0 0 0 0 0 12 12 12 3 0 | 0 0 0 0 0 0 0 4 4 3 0 0 | * * * * * * * 20 * * | 1 0 0 0 1 . o3x . x3o3o ♦ 12 | 0 12 18 | 0 0 0 4 18 0 12 | 0 0 0 0 0 6 0 12 0 3 | 0 0 0 0 0 0 0 0 4 0 3 0 | * * * * * * * * 20 * | 0 1 0 0 1 . . x o3x3o3o ♦ 20 | 0 10 60 | 0 0 0 0 30 20 40 | 0 0 0 0 0 0 10 20 10 10 | 0 0 0 0 0 0 0 0 0 5 5 2 | * * * * * * * * * 12 | 0 0 0 1 1 --------------+-----+-------------+--------------------------+--------------------------------------+--------------------------------------+-------------------------------+---------- x3o3x o3x3o . ♦ 72 | 72 72 144 | 24 36 144 24 144 48 48 | 6 48 72 48 48 48 48 48 12 0 | 12 16 16 24 24 12 0 16 16 12 0 0 | 4 4 4 0 6 0 0 4 0 0 | 5 * * * * x3o3x . x3o3o ♦ 48 | 48 48 72 | 16 24 72 16 72 0 48 | 4 24 36 0 48 24 0 48 0 12 | 6 0 16 0 24 0 12 0 16 0 12 0 | 0 4 0 4 0 6 0 0 4 0 | * 5 * * * x3o . o3x3o3o ♦ 30 | 30 0 90 | 10 0 90 0 0 30 60 | 0 30 0 30 60 0 0 0 15 15 | 0 10 20 0 0 15 15 0 0 0 0 3 | 0 0 5 5 0 0 3 0 0 0 | * * 4 * * x . x o3x3o3o ♦ 40 | 20 20 120 | 0 10 60 0 60 40 80 | 0 0 30 20 40 0 20 40 20 20 | 0 0 0 10 20 10 10 0 0 10 10 4 | 0 0 0 0 5 5 2 0 0 2 | * * * 6 * . o3x o3x3o3o ♦ 30 | 0 30 90 | 0 0 0 10 90 30 60 | 0 0 0 0 0 30 30 60 15 15 | 0 0 0 0 0 0 0 10 20 15 15 3 | 0 0 0 0 0 0 0 5 5 3 | * * * * 4
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