Acronym octike
Name octahedron-icosahedron duoprism
Circumradius sqrt[(9+sqrt(5))/8] = 1.185120

Incidence matrix according to Dynkin symbol

x3o4o x3o5o

. . . . . . | 72 |   4   5 |  4  20   5 |  1  20  20 1 |  5  20  4 |  5 4
------------+----+---------+------------+--------------+-----------+-----
x . . . . . |  2 | 144   * |  2   5   0 |  1  10   5 0 |  5  10  1 |  5 2
. . . x . . |  2 |   * 180 |  0   4   2 |  0   4   8 1 |  1   8  4 |  2 4
------------+----+---------+------------+--------------+-----------+-----
x3o . . . . |  3 |   3   0 | 96   *   * |  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 |  *   * 120 |  0   0   4 1 |  0   4  4 |  1 4
------------+----+---------+------------+--------------+-----------+-----
x3o4o . . .   6 |  12   0 |  8   0   0 | 12   *   * * |  5   0  0 |  5 0
x3o . x . .   6 |   6   3 |  2   3   0 |  * 240   * * |  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 |  *   *   * 6 |  0   0  4 |  0 4
------------+----+---------+------------+--------------+-----------+-----
x3o4o x . .  12 |  24   6 | 16  12   0 |  2   8   0 0 | 30   *  * |  2 0
x3o . x3o .   9 |   9   9 |  3   9   3 |  0   3   3 0 |  * 160  * |  1 1
x . . x3o5o  24 |  12  60 |  0  30  40 |  0   0  20 2 |  *   * 12 |  0 2
------------+----+---------+------------+--------------+-----------+-----
x3o4o x3o .  18 |  36  18 | 24  36   6 |  3  24  12 0 |  3   8  0 | 20 *
x3o . x3o5o  36 |  36  90 | 12  90  60 |  0  30  60 3 |  0  20  3 |  * 8

o3x3o x3o5o

. . . . . . | 72 |   4   5 |  2  2  20   5 |  1  10  10  20 1 |  5 10 10  4 |  5 2 2
------------+----+---------+---------------+------------------+-------------+-------
. x . . . . |  2 | 144   * |  1  1   5   0 |  1   5   5   5 0 |  5  5  5  1 |  5 1 1
. . . x . . |  2 |   * 180 |  0  0   4   2 |  0   2   2   8 1 |  1  4  4  4 |  2 2 2
------------+----+---------+---------------+------------------+-------------+-------
o3x . . . . |  3 |   3   0 | 48  *   *   * |  1   5   0   0 0 |  5  5  0  0 |  5 1 0
. x3o . . . |  3 |   3   0 |  * 48   *   * |  1   0   5   0 0 |  5  0  5  0 |  5 0 1
. x . x . . |  4 |   2   2 |  *  * 360   * |  0   1   1   2 0 |  1  2  2  1 |  2 1 1
. . . x3o . |  3 |   0   3 |  *  *   * 120 |  0   0   0   4 1 |  0  2  2  4 |  1 2 2
------------+----+---------+---------------+------------------+-------------+-------
o3x3o . . .   6 |  12   0 |  4  4   0   0 | 12   *   *   * * |  5  0  0  0 |  5 0 0
o3x . x . .   6 |   6   3 |  2  0   3   0 |  * 120   *   * * |  1  2  0  0 |  2 1 0
. x3o x . .   6 |   6   3 |  0  2   3   0 |  *   * 120   * * |  1  0  2  0 |  2 0 1
. x . x3o .   6 |   3   6 |  0  0   3   2 |  *   *   * 240 * |  0  1  1  1 |  1 1 1
. . . x3o5o  12 |   0  30 |  0  0   0  20 |  *   *   *   * 6 |  0  0  0  4 |  0 2 2
------------+----+---------+---------------+------------------+-------------+-------
o3x3o x . .  12 |  24   6 |  8  8  12   0 |  2   4   4   0 0 | 30  *  *  * |  2 0 0
o3x . x3o .   9 |   9   9 |  3  0   9   3 |  0   3   0   3 0 |  * 80  *  * |  1 1 0
. x3o x3o .   9 |   9   9 |  0  3   9   3 |  0   0   3   3 0 |  *  * 80  * |  1 0 1
. x . x3o5o  24 |  12  60 |  0  0  30  40 |  0   0   0  20 2 |  *  *  * 12 |  0 1 1
------------+----+---------+---------------+------------------+-------------+-------
o3x3o x3o .  18 |  36  18 | 12 12  36   6 |  3  12  12  12 0 |  3  4  4  0 | 20 * *
o3x . x3o5o  36 |  36  90 | 12  0  90  60 |  0  30   0  60 3 |  0 20  0  3 |  * 4 *
. x3o x3o5o  36 |  36  90 |  0 12  90  60 |  0   0  30  60 3 |  0  0 20  3 |  * * 4

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