| Acronym | cubike |
| Name | cube-icosahedron duoprism |
| Circumradius | sqrt[(11+sqrt(5))/8] = 1.286277 |
| Face vector | 96, 384, 592, 440, 162, 26 |
| Confer |
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Incidence matrix according to Dynkin symbol
o3o4x x3o5o . . . . . . | 96 | 3 5 | 3 15 5 | 1 15 15 1 | 5 15 3 | 5 3 ------------+----+---------+------------+--------------+-----------+----- . . x . . . | 2 | 144 * | 2 5 0 | 1 10 5 0 | 5 10 1 | 5 2 . . . x . . | 2 | * 240 | 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3 ------------+----+---------+------------+--------------+-----------+----- . o4x . . . | 4 | 4 0 | 72 * * | 1 5 0 0 | 5 5 0 | 5 1 . . x x . . | 4 | 2 2 | * 360 * | 0 2 2 0 | 1 4 1 | 2 2 . . . x3o . | 3 | 0 3 | * * 160 | 0 0 3 1 | 0 3 3 | 1 3 ------------+----+---------+------------+--------------+-----------+----- o3o4x . . . ♦ 8 | 12 0 | 6 0 0 | 12 * * * | 5 0 0 | 5 0 . o4x x . . ♦ 8 | 8 4 | 2 4 0 | * 180 * * | 1 2 0 | 2 1 . . x x3o . ♦ 6 | 3 6 | 0 3 2 | * * 240 * | 0 2 1 | 1 2 . . . x3o5o ♦ 12 | 0 30 | 0 0 20 | * * * 8 | 0 0 3 | 0 3 ------------+----+---------+------------+--------------+-----------+----- o3o4x x . . ♦ 16 | 24 8 | 12 12 0 | 2 6 0 0 | 30 * * | 2 0 . o4x x3o . ♦ 12 | 12 12 | 3 12 4 | 0 3 4 0 | * 120 * | 1 1 . . x x3o5o ♦ 24 | 12 60 | 0 30 40 | 0 0 20 2 | * * 12 | 0 2 ------------+----+---------+------------+--------------+-----------+----- o3o4x x3o . ♦ 24 | 36 24 | 18 36 8 | 3 18 12 0 | 3 6 0 | 20 * . o4x x3o5o ♦ 48 | 48 120 | 12 120 80 | 0 30 80 4 | 0 20 4 | * 6
x x4o x3o5o . . . . . . | 96 | 1 2 5 | 2 5 1 10 5 | 1 10 5 5 10 1 | 5 10 1 5 2 | 5 2 1 ------------+----+-----------+-------------------+--------------------+--------------+------- x . . . . . | 2 | 48 * * | 2 5 0 0 0 | 1 10 5 0 0 0 | 5 10 1 0 0 | 5 2 0 . x . . . . | 2 | * 96 * | 1 0 1 5 0 | 1 5 0 5 5 0 | 5 5 0 5 1 | 5 1 1 . . . x . . | 2 | * * 240 | 0 1 0 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1 ------------+----+-----------+-------------------+--------------------+--------------+------- x x . . . . | 4 | 2 2 0 | 48 * * * * | 1 5 0 0 0 0 | 5 5 0 0 0 | 5 1 0 x . . x . . | 4 | 2 0 2 | * 120 * * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0 . x4o . . . | 4 | 0 4 0 | * * 24 * * | 1 0 0 5 0 0 | 5 0 0 5 0 | 5 0 1 . x . x . . | 4 | 0 2 2 | * * * 240 * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1 . . . x3o . | 3 | 0 0 3 | * * * * 160 | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1 ------------+----+-----------+-------------------+--------------------+--------------+------- x x4o . . . ♦ 8 | 4 8 0 | 4 0 2 0 0 | 12 * * * * * | 5 0 0 0 0 | 5 0 0 x x . x . . ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 120 * * * * | 1 2 0 0 0 | 2 1 0 x . . x3o . ♦ 6 | 3 0 6 | 0 3 0 0 2 | * * 80 * * * | 0 2 1 0 0 | 1 2 0 . x4o x . . ♦ 8 | 0 8 4 | 0 0 2 4 0 | * * * 60 * * | 1 0 0 2 0 | 2 0 1 . x . x3o . ♦ 6 | 0 3 6 | 0 0 0 3 2 | * * * * 160 * | 0 1 0 1 1 | 1 1 1 . . . x3o5o ♦ 12 | 0 0 30 | 0 0 0 0 20 | * * * * * 8 | 0 0 1 0 2 | 0 2 1 ------------+----+-----------+-------------------+--------------------+--------------+------- x x4o x . . ♦ 16 | 8 16 8 | 8 4 4 8 0 | 2 4 0 2 0 0 | 30 * * * * | 2 0 0 x x . x3o . ♦ 12 | 6 6 12 | 3 6 0 6 4 | 0 3 2 0 2 0 | * 80 * * * | 1 1 0 x . . x3o5o ♦ 24 | 12 0 60 | 0 30 0 0 40 | 0 0 20 0 0 2 | * * 4 * * | 0 2 0 . x4o x3o . ♦ 12 | 0 12 12 | 0 0 3 12 4 | 0 0 0 3 4 0 | * * * 40 * | 1 0 1 . x . x3o5o ♦ 24 | 0 12 60 | 0 0 0 30 40 | 0 0 0 0 20 2 | * * * * 8 | 0 1 1 ------------+----+-----------+-------------------+--------------------+--------------+------- x x4o x3o . ♦ 24 | 12 24 24 | 12 12 6 24 8 | 3 12 4 6 8 0 | 3 4 0 2 0 | 20 * * x x . x3o5o ♦ 48 | 24 24 120 | 12 60 0 60 80 | 0 30 40 0 40 4 | 0 20 2 0 2 | * 4 * . x4o x3o5o ♦ 48 | 0 48 120 | 0 0 12 120 80 | 0 0 0 30 80 4 | 0 0 0 20 4 | * * 2
x x x x3o5o . . . . . . | 96 | 1 1 1 5 | 1 1 5 1 5 5 5 | 1 5 5 5 5 5 5 1 | 5 5 5 1 5 1 1 | 5 1 1 1 ------------+----+--------------+--------------------------+------------------------+-------------------+--------- x . . . . . | 2 | 48 * * * | 1 1 5 0 0 0 0 | 1 5 5 5 0 0 0 0 | 5 5 5 1 0 0 0 | 5 1 1 0 . x . . . . | 2 | * 48 * * | 1 0 0 1 5 0 0 | 1 5 0 0 5 5 0 0 | 5 5 0 0 5 1 0 | 5 1 0 1 . . x . . . | 2 | * * 48 * | 0 1 0 1 0 5 0 | 1 0 5 0 5 0 5 0 | 5 0 5 0 5 0 1 | 5 0 1 1 . . . x . . | 2 | * * * 240 | 0 0 1 0 1 1 2 | 0 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ------------+----+--------------+--------------------------+------------------------+-------------------+--------- x x . . . . | 4 | 2 2 0 0 | 24 * * * * * * | 1 5 0 0 0 0 0 0 | 5 5 0 0 0 0 0 | 5 1 0 0 x . x . . . | 4 | 2 0 2 0 | * 24 * * * * * | 1 0 5 0 0 0 0 0 | 5 0 5 0 0 0 0 | 5 0 1 0 x . . x . . | 4 | 2 0 0 2 | * * 120 * * * * | 0 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x x . . . | 4 | 0 2 2 0 | * * * 24 * * * | 1 0 0 0 5 0 0 0 | 5 0 0 0 5 0 0 | 5 0 0 1 . x . x . . | 4 | 0 2 0 2 | * * * * 120 * * | 0 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x x . . | 4 | 0 0 2 2 | * * * * * 120 * | 0 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x3o . | 3 | 0 0 0 3 | * * * * * * 160 | 0 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ------------+----+--------------+--------------------------+------------------------+-------------------+--------- x x x . . . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 0 | 12 * * * * * * * | 5 0 0 0 0 0 0 | 5 0 0 0 x x . x . . ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 | * 60 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x x . . ♦ 8 | 4 0 4 4 | 0 2 2 0 0 2 0 | * * 60 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x3o . ♦ 6 | 3 0 0 6 | 0 0 3 0 0 0 2 | * * * 80 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x x x . . ♦ 8 | 0 4 4 4 | 0 0 0 2 2 2 0 | * * * * 60 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x3o . ♦ 6 | 0 3 0 6 | 0 0 0 0 3 0 2 | * * * * * 80 * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x x3o . ♦ 6 | 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * 80 * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x3o5o ♦ 12 | 0 0 0 30 | 0 0 0 0 0 0 20 | * * * * * * * 8 | 0 0 0 1 0 1 1 | 0 1 1 1 ------------+----+--------------+--------------------------+------------------------+-------------------+--------- x x x x . . ♦ 16 | 8 8 8 8 | 4 4 4 4 4 4 0 | 2 2 2 0 2 0 0 0 | 30 * * * * * * | 2 0 0 0 x x . x3o . ♦ 12 | 6 6 0 12 | 3 0 6 0 6 0 4 | 0 3 0 2 0 2 0 0 | * 40 * * * * * | 1 1 0 0 x . x x3o . ♦ 12 | 6 0 6 12 | 0 3 6 0 0 6 4 | 0 0 3 2 0 0 2 0 | * * 40 * * * * | 1 0 1 0 x . . x3o5o ♦ 24 | 12 0 0 60 | 0 0 30 0 0 0 40 | 0 0 0 20 0 0 0 2 | * * * 4 * * * | 0 1 1 0 . x x x3o . ♦ 12 | 0 6 6 12 | 0 0 0 3 6 6 4 | 0 0 0 0 3 2 2 0 | * * * * 40 * * | 1 0 0 1 . x . x3o5o ♦ 24 | 0 12 0 60 | 0 0 0 0 30 0 40 | 0 0 0 0 0 20 0 2 | * * * * * 4 * | 0 1 0 1 . . x x3o5o ♦ 24 | 0 0 12 60 | 0 0 0 0 0 30 40 | 0 0 0 0 0 0 20 2 | * * * * * * 4 | 0 0 1 1 ------------+----+--------------+--------------------------+------------------------+-------------------+--------- x x x x3o . ♦ 24 | 12 12 12 24 | 6 6 12 6 12 12 8 | 3 6 6 4 6 4 4 0 | 3 2 2 0 2 0 0 | 20 * * * x x . x3o5o ♦ 48 | 24 24 0 120 | 12 0 60 0 60 0 80 | 0 30 0 40 0 40 0 4 | 0 20 0 2 0 2 0 | * 2 * * x . x x3o5o ♦ 48 | 24 0 24 120 | 0 12 60 0 0 60 80 | 0 0 30 40 0 0 40 4 | 0 0 20 2 0 0 2 | * * 2 * . x x x3o5o ♦ 48 | 0 24 24 120 | 0 0 0 12 60 60 80 | 0 0 0 0 30 40 40 4 | 0 0 0 0 20 2 2 | * * * 2
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