Acronym cubid
Name cube-icosidodecahedron duoprism
Circumradius sqrt[9+2 sqrt(5)]/2 = 1.835220

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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