Acronym octdoe
Name octahedron-dodecahedron duoprism
Circumradius sqrt[(13+3 sqrt(5))/8] = 1.569562

Incidence matrix according to Dynkin symbol

x3o4o o3o5x

. . . . . . | 120 |   4   3 |   4  12  3 |  1  12  12 1 |  3 12  4 |  3 4
------------+-----+---------+------------+--------------+----------+-----
x . . . . . |   2 | 240   * |   2   3  0 |  1   6   3 0 |  3  6  1 |  3 2
. . . . . x |   2 |   * 180 |   0   4  2 |  0   4   8 1 |  1  8  4 |  2 4
------------+-----+---------+------------+--------------+----------+-----
x3o . . . . |   3 |   3   0 | 160   *  * |  1   3   0 0 |  3  3  0 |  3 1
x . . . . x |   4 |   2   2 |   * 360  * |  0   2   2 0 |  1  4  1 |  2 2
. . . . o5x |   5 |   0   5 |   *   * 72 |  0   0   4 1 |  0  4  4 |  1 4
------------+-----+---------+------------+--------------+----------+-----
x3o4o . . .    6 |  12   0 |   8   0  0 | 20   *   * * |  3  0  0 |  3 0
x3o . . . x    6 |   6   3 |   2   3  0 |  * 240   * * |  1  2  0 |  2 1
x . . . o5x   10 |   5  10 |   0   5  2 |  *   * 144 * |  0  2  1 |  1 2
. . . o3o5x   20 |   0  30 |   0   0 12 |  *   *   * 6 |  0  0  4 |  0 4
------------+-----+---------+------------+--------------+----------+-----
x3o4o . . x   12 |  24   6 |  16  12  0 |  2   8   0 0 | 30  *  * |  2 0
x3o . . o5x   15 |  15  15 |   5  15  3 |  0   5   3 0 |  * 96  * |  1 1
x . . o3o5x   40 |  20  60 |   0  30 24 |  0   0  12 2 |  *  * 12 |  0 2
------------+-----+---------+------------+--------------+----------+-----
x3o4o . o5x   30 |  60  30 |  40  60  6 |  5  40  12 0 |  5  8  0 | 12 *
x3o . o3o5x   60 |  60  90 |  20  90 36 |  0  30  36 3 |  0 12  3 |  * 8

o3x3o o3o5x

. . . . . . | 120 |   4   3 |  2  2  12  3 |  1   6   6  12 1 |  3  6  6  4 |  3 2 2
------------+-----+---------+--------------+------------------+-------------+-------
. x . . . . |   2 | 240   * |  1  1   3  0 |  1   3   3   3 0 |  3  3  3  1 |  3 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 | 80  *   *  * |  1   3   0   0 0 |  3  3  0  0 |  3 1 0
. x3o . . . |   3 |   3   0 |  * 80   *  * |  1   0   3   0 0 |  3  0  3  0 |  3 0 1
. x . . . x |   4 |   2   2 |  *  * 360  * |  0   1   1   2 0 |  1  2  2  1 |  2 1 1
. . . . o5x |   5 |   0   5 |  *  *   * 72 |  0   0   0   4 1 |  0  2  2  4 |  1 2 2
------------+-----+---------+--------------+------------------+-------------+-------
o3x3o . . .    6 |  12   0 |  4  4   0  0 | 20   *   *   * * |  3  0  0  0 |  3 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 . . o5x   10 |   5  10 |  0  0   5  2 |  *   *   * 144 * |  0  1  1  1 |  1 1 1
. . . o3o5x   20 |   0  30 |  0  0   0 12 |  *   *   *   * 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 . . o5x   15 |  15  15 |  5  0  15  3 |  0   5   0   3 0 |  * 48  *  * |  1 1 0
. x3o . o5x   15 |  15  15 |  0  5  15  3 |  0   0   5   3 0 |  *  * 48  * |  1 0 1
. x . o3o5x   40 |  20  60 |  0  0  30 24 |  0   0   0  12 2 |  *  *  * 12 |  0 1 1
------------+-----+---------+--------------+------------------+-------------+-------
o3x3o . o5x   30 |  60  30 | 20 20  60  6 |  5  20  20  12 0 |  5  4  4  0 | 12 * *
o3x . o3o5x   60 |  60  90 | 20  0  90 36 |  0  30   0  36 3 |  0 12  0  3 |  * 4 *
. x3o o3o5x   60 |  60  90 |  0 20  90 36 |  0   0  30  36 3 |  0  0 12  3 |  * * 4

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