Acronym | octid |
Name | octahedron-icosidodecahedron duoprism |
Circumradius | sqrt[(4+sqrt(5))/2] = 1.765796 |
Face vector | 180, 720, 1152, 900, 328, 40 |
Confer |
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Incidence matrix according to Dynkin symbol
x3o4o o3x5o . . . . . . | 180 | 4 4 | 4 16 2 2 | 1 16 8 8 1 | 4 8 8 4 | 2 2 4 ------------+-----+---------+----------------+------------------+--------------+-------- x . . . . . | 2 | 360 * | 2 4 0 0 | 1 8 2 2 0 | 4 4 4 1 | 2 2 2 . . . . x . | 2 | * 360 | 0 4 1 1 | 0 4 4 4 1 | 1 4 4 4 | 1 1 4 ------------+-----+---------+----------------+------------------+--------------+-------- x3o . . . . | 3 | 3 0 | 240 * * * | 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 | * * 120 * | 0 0 4 0 1 | 0 4 0 4 | 1 0 4 . . . . x5o | 5 | 0 5 | * * * 72 | 0 0 0 4 1 | 0 0 4 4 | 0 1 4 ------------+-----+---------+----------------+------------------+--------------+-------- x3o4o . . . ♦ 6 | 12 0 | 8 0 0 0 | 30 * * * * | 4 0 0 0 | 2 2 0 x3o . . x . ♦ 6 | 6 3 | 2 3 0 0 | * 480 * * * | 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 | * * * * 6 | 0 0 0 4 | 0 0 4 ------------+-----+---------+----------------+------------------+--------------+-------- x3o4o . x . ♦ 12 | 24 6 | 16 12 0 0 | 2 8 0 0 0 | 60 * * * | 1 1 0 x3o . o3x . ♦ 9 | 9 9 | 3 9 3 0 | 0 3 3 0 0 | * 160 * * | 1 0 1 x3o . . x5o ♦ 15 | 15 15 | 5 15 0 3 | 0 5 0 3 0 | * * 96 * | 0 1 1 x . . o3x5o ♦ 60 | 30 120 | 0 60 40 24 | 0 0 20 12 2 | * * * 12 | 0 0 2 ------------+-----+---------+----------------+------------------+--------------+-------- x3o4o o3x . ♦ 18 | 36 18 | 24 36 6 0 | 3 24 12 0 0 | 3 8 0 0 | 20 * * x3o4o . x5o ♦ 30 | 60 30 | 40 60 0 6 | 5 40 0 12 0 | 5 0 8 0 | * 12 * x3o . o3x5o ♦ 90 | 90 180 | 30 180 60 36 | 0 60 60 36 3 | 0 20 12 3 | * * 8
o3x3o o3x5o . . . . . . | 180 | 4 4 | 2 2 16 2 2 | 1 8 8 8 8 1 | 4 4 4 4 4 4 | 2 2 2 2 ------------+-----+---------+--------------------+----------------------+-------------------+---------- . x . . . . | 2 | 360 * | 1 1 4 0 0 | 1 4 4 2 2 0 | 4 2 2 2 2 1 | 2 2 1 1 . . . . x . | 2 | * 360 | 0 0 4 1 1 | 0 2 2 4 4 1 | 1 2 2 2 2 4 | 1 1 2 2 ------------+-----+---------+--------------------+----------------------+-------------------+---------- o3x . . . . | 3 | 3 0 | 120 * * * * | 1 4 0 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0 . x3o . . . | 3 | 3 0 | * 120 * * * | 1 0 4 0 0 0 | 4 0 0 2 2 0 | 2 2 0 1 . x . . x . | 4 | 2 2 | * * 720 * * | 0 1 1 1 1 0 | 1 1 1 1 1 1 | 1 1 1 1 . . . o3x . | 3 | 0 3 | * * * 120 * | 0 0 0 4 0 1 | 0 2 0 2 0 4 | 1 0 2 2 . . . . x5o | 5 | 0 5 | * * * * 72 | 0 0 0 0 4 1 | 0 0 2 0 2 4 | 0 1 2 2 ------------+-----+---------+--------------------+----------------------+-------------------+---------- o3x3o . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 30 * * * * * | 4 0 0 0 0 0 | 2 2 0 0 o3x . . x . ♦ 6 | 6 3 | 2 0 3 0 0 | * 240 * * * * | 1 1 1 0 0 0 | 1 1 1 0 . x3o . x . ♦ 6 | 6 3 | 0 2 3 0 0 | * * 240 * * * | 1 0 0 1 1 0 | 1 1 0 1 . x . o3x . ♦ 6 | 3 6 | 0 0 3 2 0 | * * * 240 * * | 0 1 0 1 0 1 | 1 0 1 1 . x . . x5o ♦ 10 | 5 10 | 0 0 5 0 2 | * * * * 144 * | 0 0 1 0 1 1 | 0 1 1 1 . . . o3x5o ♦ 30 | 0 60 | 0 0 0 20 12 | * * * * * 6 | 0 0 0 0 0 4 | 0 0 2 2 ------------+-----+---------+--------------------+----------------------+-------------------+---------- o3x3o . x . ♦ 12 | 24 6 | 8 8 12 0 0 | 2 4 4 0 0 0 | 60 * * * * * | 1 1 0 0 o3x . o3x . ♦ 9 | 9 9 | 3 0 9 3 0 | 0 3 0 3 0 0 | * 80 * * * * | 1 0 1 0 o3x . . x5o ♦ 15 | 15 15 | 5 0 15 0 3 | 0 5 0 0 3 0 | * * 48 * * * | 0 1 1 0 . x3o o3x . ♦ 9 | 9 9 | 0 3 9 3 0 | 0 0 3 3 0 0 | * * * 80 * * | 1 0 0 1 . x3o . x5o ♦ 15 | 15 15 | 0 5 15 0 3 | 0 0 5 0 3 0 | * * * * 48 * | 0 1 0 1 . x . o3x5o ♦ 60 | 30 120 | 0 0 60 40 24 | 0 0 0 20 12 2 | * * * * * 12 | 0 0 1 1 ------------+-----+---------+--------------------+----------------------+-------------------+---------- o3x3o o3x . ♦ 18 | 36 18 | 12 12 36 6 0 | 3 12 12 12 0 0 | 3 4 0 4 0 0 | 20 * * * o3x3o . x5o ♦ 30 | 60 30 | 20 20 60 0 6 | 5 20 20 0 12 0 | 5 0 4 0 4 0 | * 12 * * o3x . o3x5o ♦ 90 | 90 180 | 30 0 180 60 36 | 0 60 0 60 36 3 | 0 20 12 0 0 3 | * * 4 * . x3o o3x5o ♦ 90 | 90 180 | 0 30 180 60 36 | 0 0 60 60 36 3 | 0 0 0 20 12 3 | * * * 4
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