| Acronym | cubid |
| Name | cube-icosidodecahedron duoprism |
| Circumradius | sqrt[9+2 sqrt(5)]/2 = 1.835220 |
| Face vector | 240, 840, 1156, 782, 264, 38 |
| Confer |
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Incidence matrix according to Dynkin symbol
o3o4x o3x5o . . . . . . | 240 | 3 4 | 3 12 2 2 | 1 12 6 6 1 | 4 6 6 3 | 2 2 3 ------------+-----+---------+----------------+------------------+--------------+-------- . . x . . . | 2 | 360 * | 2 4 0 0 | 1 8 2 2 0 | 4 4 4 1 | 2 2 2 . . . . x . | 2 | * 480 | 0 3 1 1 | 0 3 3 3 1 | 1 3 3 3 | 1 1 3 ------------+-----+---------+----------------+------------------+--------------+-------- . o4x . . . | 4 | 4 0 | 180 * * * | 1 4 0 0 0 | 4 2 2 0 | 2 2 1 . . x . x . | 4 | 2 2 | * 720 * * | 0 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . o3x . | 3 | 0 3 | * * 160 * | 0 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x5o | 5 | 0 5 | * * * 96 | 0 0 0 3 1 | 0 0 3 3 | 0 1 3 ------------+-----+---------+----------------+------------------+--------------+-------- o3o4x . . . ♦ 8 | 12 0 | 6 0 0 0 | 30 * * * * | 4 0 0 0 | 2 2 0 . o4x . x . ♦ 8 | 8 4 | 2 4 0 0 | * 360 * * * | 1 1 1 0 | 1 1 1 . . x o3x . ♦ 6 | 3 6 | 0 3 2 0 | * * 240 * * | 0 2 0 1 | 1 0 2 . . x . x5o ♦ 10 | 5 10 | 0 5 0 2 | * * * 144 * | 0 0 2 1 | 0 1 2 . . . o3x5o ♦ 30 | 0 60 | 0 0 20 12 | * * * * 8 | 0 0 0 3 | 0 0 3 ------------+-----+---------+----------------+------------------+--------------+-------- o3o4x . x . ♦ 16 | 24 8 | 12 12 0 0 | 2 6 0 0 0 | 60 * * * | 1 1 0 . o4x o3x . ♦ 12 | 12 12 | 3 12 4 0 | 0 3 4 0 0 | * 120 * * | 1 0 1 . o4x . x5o ♦ 20 | 20 20 | 5 20 0 4 | 0 5 0 4 0 | * * 72 * | 0 1 1 . . x o3x5o ♦ 60 | 30 120 | 0 60 40 24 | 0 0 20 12 2 | * * * 12 | 0 0 2 ------------+-----+---------+----------------+------------------+--------------+-------- o3o4x o3x . ♦ 24 | 36 24 | 18 36 8 0 | 3 18 12 0 0 | 3 6 0 0 | 20 * * o3o4x . x5o ♦ 40 | 60 40 | 30 60 0 8 | 5 30 0 12 0 | 5 0 6 0 | * 12 * . o4x o3x4o ♦ 120 | 120 240 | 30 240 80 48 | 0 60 80 48 4 | 0 20 12 4 | * * 6
x x4o o3x5o . . . . . . | 240 | 1 2 4 | 2 4 1 8 2 2 | 1 8 2 2 4 4 4 1 | 4 4 4 1 2 2 2 | 2 2 2 1 ------------+-----+-------------+-----------------------+---------------------------+--------------------+---------- x . . . . . | 2 | 120 * * | 2 4 0 0 0 0 | 1 8 2 2 0 0 0 0 | 4 4 4 1 0 0 0 | 2 2 2 0 . x . . . . | 2 | * 240 * | 1 0 1 4 0 0 | 1 4 0 0 4 2 2 0 | 4 2 2 0 2 2 1 | 2 2 1 1 . . . . x . | 2 | * * 480 | 0 1 0 2 1 1 | 0 2 1 1 1 2 2 1 | 1 2 2 1 1 1 2 | 1 1 2 1 ------------+-----+-------------+-----------------------+---------------------------+--------------------+---------- x x . . . . | 4 | 2 2 0 | 120 * * * * * | 1 4 0 0 0 0 0 0 | 4 2 2 0 0 0 0 | 2 2 1 0 x . . . x . | 4 | 2 0 2 | * 240 * * * * | 0 2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0 . x4o . . . | 4 | 0 4 0 | * * 60 * * * | 1 0 0 0 4 0 0 0 | 4 0 0 0 2 2 0 | 2 2 0 1 . x . . x . | 4 | 0 2 2 | * * * 480 * * | 0 1 0 0 1 1 1 0 | 1 1 1 0 1 1 1 | 1 1 1 1 . . . o3x . | 3 | 0 0 3 | * * * * 160 * | 0 0 1 0 0 2 0 1 | 0 2 0 1 1 0 2 | 1 0 2 1 . . . . x5o | 5 | 0 0 5 | * * * * * 96 | 0 0 0 1 0 0 2 1 | 0 0 2 1 0 1 2 | 0 1 2 1 ------------+-----+-------------+-----------------------+---------------------------+--------------------+---------- x x4o . . . ♦ 8 | 4 8 0 | 4 0 2 0 0 0 | 30 * * * * * * * | 4 0 0 0 0 0 0 | 2 2 0 0 x x . . x . ♦ 8 | 4 4 4 | 2 2 0 2 0 0 | * 240 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 x . . o3x . ♦ 6 | 3 0 6 | 0 3 0 0 2 0 | * * 80 * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0 x . . . x5o ♦ 10 | 5 0 10 | 0 5 0 0 0 2 | * * * 48 * * * * | 0 0 2 1 0 0 0 | 0 1 2 0 . x4o . x . ♦ 8 | 0 8 4 | 0 0 2 4 0 0 | * * * * 120 * * * | 1 0 0 0 1 1 0 | 1 1 0 1 . x . o3x . ♦ 6 | 0 3 6 | 0 0 0 3 2 0 | * * * * * 120 * * | 0 1 0 0 1 0 1 | 1 0 1 1 . x . . x50 ♦ 10 | 0 5 10 | 0 0 0 5 0 2 | * * * * * * 96 * | 0 0 1 0 0 1 1 | 0 1 1 1 . . . o3x5o ♦ 30 | 0 0 60 | 0 0 0 0 20 12 | * * * * * * * 8 | 0 0 0 1 0 0 2 | 0 0 2 1 ------------+-----+-------------+-----------------------+---------------------------+--------------------+---------- x x4o . x . ♦ 16 | 8 16 8 | 8 4 4 8 0 0 | 2 4 0 0 2 0 0 0 | 60 * * * * * * | 1 1 0 0 x x . o3x . ♦ 12 | 6 6 12 | 3 6 0 6 4 0 | 0 3 2 0 0 2 0 0 | * 80 * * * * * | 1 0 1 0 x x . . x5o ♦ 20 | 10 10 20 | 5 10 0 10 0 4 | 0 5 0 2 0 0 2 0 | * * 48 * * * * | 0 1 1 0 x . . o3x5o ♦ 60 | 30 0 120 | 0 60 0 0 40 24 | 0 0 20 12 0 0 0 2 | * * * 4 * * * | 0 0 2 0 . x4o o3x . ♦ 12 | 0 12 12 | 0 0 3 12 4 0 | 0 0 0 0 3 4 0 0 | * * * * 40 * * | 1 0 0 1 . x4o . x5o ♦ 20 | 0 20 20 | 0 0 5 20 0 4 | 0 0 0 0 5 0 4 0 | * * * * * 24 * | 0 1 0 1 . x . o3x5o ♦ 60 | 0 30 120 | 0 0 0 60 40 24 | 0 0 0 0 0 20 12 2 | * * * * * * 8 | 0 0 1 1 ------------+-----+-------------+-----------------------+---------------------------+--------------------+---------- x x4o o3x . ♦ 24 | 12 24 24 | 12 12 6 24 8 0 | 3 12 4 0 6 8 0 0 | 3 4 0 0 2 0 0 | 20 * * * x x4o . x5o ♦ 40 | 20 40 40 | 20 20 10 40 0 8 | 5 20 0 4 10 0 8 0 | 5 0 4 0 0 2 0 | * 12 * * x x . o3x5o ♦ 120 | 60 60 240 | 30 120 0 120 80 48 | 0 60 40 24 0 40 24 4 | 0 20 12 2 0 0 2 | * * 4 * . x4o o3x5o ♦ 120 | 0 120 240 | 0 0 30 240 80 48 | 0 0 0 0 60 80 48 4 | 0 0 0 0 20 12 4 | * * * 2
x x x o3x5o . . . . . . | 240 | 1 1 1 4 | 1 1 4 1 4 4 2 2 | 1 4 4 2 2 4 2 2 2 2 1 | 4 2 2 2 2 1 2 2 1 1 | 2 2 1 1 1 ------------+-----+-----------------+-----------------------------+------------------------------------+----------------------------+------------ x . . . . . | 2 | 120 * * * | 1 1 4 0 0 0 0 0 | 1 4 4 2 2 0 0 0 0 0 0 | 4 2 2 2 2 1 0 0 0 0 | 2 2 1 1 0 . x . . . . | 2 | * 120 * * | 1 0 0 1 4 0 0 0 | 1 4 0 0 0 4 2 2 0 0 0 | 4 2 2 0 0 0 2 2 1 0 | 2 2 1 0 1 . . x . . . | 2 | * * 120 * | 0 1 0 1 0 4 0 0 | 1 0 4 0 0 4 0 0 2 2 0 | 4 0 0 2 2 0 2 2 0 1 | 2 2 0 1 1 . . . . x . | 2 | * * * 480 | 0 0 1 0 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 ------------+-----+-----------------+-----------------------------+------------------------------------+----------------------------+------------ x x . . . . | 4 | 2 2 0 0 | 60 * * * * * * * | 1 4 0 0 0 0 0 0 0 0 0 | 4 2 2 0 0 0 0 0 0 0 | 2 2 1 0 0 x . x . . . | 4 | 2 0 2 0 | * 60 * * * * * * | 1 0 4 0 0 0 0 0 0 0 0 | 4 0 0 2 2 0 0 0 0 0 | 2 2 0 1 0 x . . . x . | 4 | 2 0 0 2 | * * 240 * * * * * | 0 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 . x x . . . | 4 | 0 2 2 0 | * * * 60 * * * * | 1 0 0 0 0 4 0 0 0 0 0 | 4 0 0 0 0 0 2 2 0 0 | 2 2 0 0 1 . x . . x . | 4 | 0 2 0 2 | * * * * 240 * * * | 0 1 0 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 . . x . x . | 4 | 0 0 2 2 | * * * * * 240 * * | 0 0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . o3x . | 3 | 0 0 0 3 | * * * * * * 160 * | 0 0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1 . . . . x5o | 5 | 0 0 0 5 | * * * * * * * 96 | 0 0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ------------+-----+-----------------+-----------------------------+------------------------------------+----------------------------+------------ x x x . . . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 0 0 | 30 * * * * * * * * * * | 4 0 0 0 0 0 0 0 0 0 | 2 2 0 0 0 x x . . x . ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 0 | * 120 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . x . ♦ 8 | 4 0 4 4 | 0 2 2 0 0 2 0 0 | * * 120 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . o3x . ♦ 6 | 3 0 0 6 | 0 0 3 0 0 0 2 0 | * * * 80 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 x . . . x5o ♦ 10 | 5 0 0 10 | 0 0 5 0 0 0 0 2 | * * * * 48 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x x . x . ♦ 8 | 0 4 4 4 | 0 0 0 2 2 2 0 0 | * * * * * 120 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . o3x . ♦ 6 | 0 3 0 6 | 0 0 0 0 3 0 2 0 | * * * * * * 80 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x5o ♦ 10 | 0 5 0 10 | 0 0 0 0 5 0 0 2 | * * * * * * * 48 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x o3x . ♦ 6 | 0 0 3 6 | 0 0 0 0 0 3 2 0 | * * * * * * * * 80 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x5o ♦ 10 | 0 0 5 10 | 0 0 0 0 0 5 0 2 | * * * * * * * * * 48 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . o3x5o ♦ 30 | 0 0 0 60 | 0 0 0 0 0 0 20 12 | * * * * * * * * * * 8 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ------------+-----+-----------------+-----------------------------+------------------------------------+----------------------------+------------ x x x . x . ♦ 16 | 8 8 8 8 | 4 4 4 4 4 4 0 0 | 2 2 2 0 0 2 0 0 0 0 0 | 60 * * * * * * * * * | 1 1 0 0 0 x x . o3x . ♦ 12 | 6 6 0 12 | 3 0 6 0 6 0 4 0 | 0 3 0 2 0 0 2 0 0 0 0 | * 40 * * * * * * * * | 1 0 1 0 0 x x . . x5o ♦ 20 | 10 10 0 20 | 5 0 10 0 10 0 0 4 | 0 5 0 0 2 0 0 2 0 0 0 | * * 24 * * * * * * * | 0 1 1 0 0 x . x o3x . ♦ 12 | 6 0 6 12 | 0 3 6 0 0 6 4 0 | 0 0 3 2 0 0 0 0 2 0 0 | * * * 40 * * * * * * | 1 0 0 1 0 x . x . x5o ♦ 20 | 10 0 10 20 | 0 5 10 0 0 10 0 4 | 0 0 5 0 2 0 0 0 0 2 0 | * * * * 24 * * * * * | 0 1 0 1 0 x . . o3x5o ♦ 60 | 30 0 0 120 | 0 0 60 0 0 0 40 24 | 0 0 0 20 12 0 0 0 0 0 2 | * * * * * 4 * * * * | 0 0 1 1 0 . x x o3x . ♦ 12 | 0 6 6 12 | 0 0 0 3 6 6 4 0 | 0 0 0 0 0 3 2 0 2 0 0 | * * * * * * 40 * * * | 1 0 0 0 1 . x x . x5o ♦ 20 | 0 10 10 20 | 0 0 0 5 10 10 0 4 | 0 0 0 0 0 5 0 2 0 2 0 | * * * * * * * 24 * * | 0 1 0 0 1 . x . o3x5o ♦ 60 | 0 30 0 120 | 0 0 0 0 60 0 40 24 | 0 0 0 0 0 0 20 12 0 0 2 | * * * * * * * * 4 * | 0 0 1 0 1 . . x o3x5o ♦ 60 | 0 0 30 120 | 0 0 0 0 0 60 40 24 | 0 0 0 0 0 0 0 0 20 12 2 | * * * * * * * * * 4 | 0 0 0 1 1 ------------+-----+-----------------+-----------------------------+------------------------------------+----------------------------+------------ x x x o3x . ♦ 24 | 12 12 12 24 | 6 6 12 6 12 12 8 0 | 3 6 6 4 0 6 4 0 4 0 0 | 3 2 0 2 0 0 2 0 0 0 | 20 * * * * x x x . x5o ♦ 40 | 20 20 20 40 | 10 10 20 10 20 20 0 8 | 5 10 10 0 4 10 0 4 0 4 0 | 5 0 2 0 2 0 0 2 0 0 | * 12 * * * x x . o3x5o ♦ 120 | 60 60 0 240 | 30 0 120 0 120 0 80 48 | 0 60 0 40 24 0 40 24 0 0 4 | 0 20 12 0 0 2 0 0 2 0 | * * 2 * * x . x o3x5o ♦ 120 | 60 0 60 240 | 0 30 120 0 0 120 80 48 | 0 0 60 40 24 0 0 0 40 24 4 | 0 0 0 20 12 2 0 0 0 2 | * * * 2 * . x x o3x5o ♦ 120 | 0 60 60 240 | 0 0 0 30 120 120 80 48 | 0 0 0 0 0 60 40 24 40 24 4 | 0 0 0 0 0 0 20 12 2 2 | * * * * 2
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