Acronym cubike
Name cube-icosahedron duoprism
Circumradius sqrt[(11+sqrt(5))/8] = 1.286277

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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