Acronym cubedoe
Name cube-dodecahedron duoprism
Circumradius sqrt[(15+3 sqrt(5))/8] = 1.647278

Incidence matrix according to Dynkin symbol

o3o4x o3o5x

. . . . . . | 160 |   3   3 |   3   9  3 |  1   9   9 1 |  3  9  3 |  3 3
------------+-----+---------+------------+--------------+----------+-----
. . x . . . |   2 | 240   * |   2   3  0 |  1   6   3 0 |  3  6  1 |  3 2
. . . . . x |   2 |   * 240 |   0   3  2 |  0   3   6 1 |  1  6  3 |  2 3
------------+-----+---------+------------+--------------+----------+-----
. o4x . . . |   4 |   4   0 | 120   *  * |  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 |   *   * 96 |  0   0   3 1 |  0  3  3 |  1 3
------------+-----+---------+------------+--------------+----------+-----
o3o4x . . .    8 |  12   0 |   6   0  0 | 20   *   * * |  3  0  0 |  3 0
. o4x . . x    8 |   8   4 |   2   4  0 |  * 180   * * |  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 |  *   *   * 8 |  0  0  3 |  0 3
------------+-----+---------+------------+--------------+----------+-----
o3o4x . . x   16 |  24   8 |  12  12  0 |  2   6   0 0 | 30  *  * |  2 0
. o4x . o5x   20 |  20  20 |   5  20  4 |  0   5   4 0 |  * 72  * |  1 1
. . x o3o5x   40 |  20  60 |   0  30 24 |  0   0  12 2 |  *  * 12 |  0 2
------------+-----+---------+------------+--------------+----------+-----
o3o4x . o5x   40 |  60  40 |  30  60  8 |  5  30  12 0 |  5  6  0 | 12 *
. o4x o3o5x   80 |  80 120 |  20 120 48 |  0  30  48 4 |  0 12  4 |  * 6

x x4o o3o5x

. . . . . . | 160 |  1   2   3 |  2   3  1   6  3 |  1   6  3  3  6 1 |  3  6 1  3 2 |  3 2 1
------------+-----+------------+------------------+-------------------+--------------+-------
x . . . . . |   2 | 80   *   * |  2   3  0   0  0 |  1   6  3  0  0 0 |  3  6 1  0 0 |  3 2 0
. x . . . . |   2 |  * 160   * |  0   0  2   3  0 |  1   3  0  3  3 0 |  3  3 0  3 1 |  3 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 | 80   *  *   *  * |  1   3  0  0  0 0 |  3  3 0  0 0 |  3 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 |  *   * 40   *  * |  1   0  0  3  0 0 |  3  0 0  3 0 |  3 0 1
. x . . . x |   4 |  0   2   2 |  *   *  * 240  * |  0   1  0  1  2 0 |  1  2 0  2 1 |  2 1 1
. . . . o5x |   5 |  0   0   5 |  *   *  *   * 96 |  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 | 20   *  *  *  * * |  3  0 0  0 0 |  3 0 0
x x . . . x    8 |  4   4   4 |  2   2  0   2  0 |  * 120  *  *  * * |  1  2 0  0 0 |  2 1 0
x . . . o5x   10 |  5   0  10 |  0   5  0   0  2 |  *   * 48  *  * * |  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 . . o5x   10 |  0   5  10 |  0   0  0   5  2 |  *   *  *  * 96 * |  0  1 0  1 1 |  1 1 1
. . . o3o5x   20 |  0   0  30 |  0   0  0   0 12 |  *   *  *  *  * 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 . . o5x   20 | 10  10  20 |  5  10  0  10  4 |  0   5  2  0  2 0 |  * 48 *  * * |  1 1 0
x . . o3o5x   40 | 20   0  60 |  0  30  0   0 24 |  0   0 12  0  0 2 |  *  * 4  * * |  0 2 0
. x4o . o5x   20 |  0  20  20 |  0   0  5  20  4 |  0   0  0  5  4 0 |  *  * * 24 * |  1 0 1
. x . o3o5x   40 |  0  20  60 |  0   0  0  30 24 |  0   0  0  0 12 2 |  *  * *  * 8 |  0 1 1
------------+-----+------------+------------------+-------------------+--------------+-------
x x4o . o5x   40 | 20  40  40 | 20  20 10  40  8 |  5  20  4 10  8 0 |  5  4 0  2 0 | 12 * *
x x . o3o5x   80 | 40  40 120 | 20  60  0  60 48 |  0  30 24  0 24 4 |  0 12 2  0 2 |  * 4 *
. x4o o3o5x   80 |  0  80 120 |  0   0 20 120 48 |  0   0  0 30 48 4 |  0  0 0 12 4 |  * * 2

x x x o3o5x

. . . . . . | 160 |  1  1  1   3 |  1  1   3  1   3   3  3 |  1  3  3  3  3  3  3 1 |  3  3  3 1  3 1 1 |  3 1 1 1
------------+-----+--------------+-------------------------+------------------------+-------------------+---------
x . . . . . |   2 | 80  *  *   * |  1  1   3  0   0   0  0 |  1  3  3  3  0  0  0 0 |  3  3  3 1  0 0 0 |  3 1 1 0
. x . . . . |   2 |  * 80  *   * |  0  0   0  2   3   0  0 |  1  3  0  0  3  3  0 0 |  3  3  0 0  3 1 0 |  3 1 0 1
. . x . . . |   2 |  *  * 80   * |  0  0   0  2   0   3  0 |  1  0  3  0  3  0  3 0 |  3  0  3 0  3 0 1 |  3 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 | 40  *   *  *   *   *  * |  1  3  0  0  0  0  0 0 |  3  3  0 0  0 0 0 |  3 1 0 0
x . x . . . |   4 |  2  0  2   0 |  * 40   *  *   *   *  * |  1  0  3  0  0  0  0 0 |  3  0  3 0  0 0 0 |  3 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 |  *  *   * 40   *   *  * |  1  0  0  0  3  0  0 0 |  3  0  0 0  3 0 0 |  3 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
. . . . o5x |   5 |  0  0  0   5 |  *  *   *  *   *   * 96 |  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 | 20  *  *  *  *  *  * * |  3  0  0 0  0 0 0 |  3 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 . . . o5x   10 |  5  0  0  10 |  0  0   5  0   0   0  2 |  *  *  * 48  *  *  * * |  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 . . o5x   10 |  0  5  0  10 |  0  0   0  0   5   0  2 |  *  *  *  *  * 48  * * |  0  1  0 0  1 1 0 |  1 1 0 1
. . x . o5x   10 |  0  0  5  10 |  0  0   0  0   0   5  2 |  *  *  *  *  *  * 48 * |  0  0  1 0  1 0 1 |  1 0 1 1
. . . o3o5x   20 |  0  0  0  30 |  0  0   0  0   0   0 12 |  *  *  *  *  *  *  * 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 . . o5x   20 | 10 10  0  20 |  5  0  10  0  10   0  4 |  0  5  0  2  0  2  0 0 |  * 24  * *  * * * |  1 1 0 0
x . x . o5x   20 | 10  0 10  20 |  0  5  10  0   0  10  4 |  0  0  5  2  0  0  2 0 |  *  * 24 *  * * * |  1 0 1 0
x . . o3o5x   40 | 20  0  0  60 |  0  0  30  0   0   0 24 |  0  0  0 12  0  0  0 2 |  *  *  * 4  * * * |  0 1 1 0
. x x . o5x   20 |  0 10 10  20 |  0  0   0  5  10  10  4 |  0  0  0  0  5  2  2 0 |  *  *  * * 24 * * |  1 0 0 1
. x . o3o5x   40 |  0 20  0  60 |  0  0   0  0  30   0 24 |  0  0  0  0  0 12  0 2 |  *  *  * *  * 4 * |  0 1 0 1
. . x o3o5x   40 |  0  0 20  60 |  0  0   0  0   0  30 24 |  0  0  0  0  0  0 12 2 |  *  *  * *  * * 4 |  0 0 1 1
------------+-----+--------------+-------------------------+------------------------+-------------------+---------
x x x . o5x   40 | 20 20 20  40 | 10 10  20 10  20  20  8 |  5 10 10  4 10  4  4 0 |  5  2  2 0  2 0 0 | 12 * * *
x x . o3o5x   80 | 40 40  0 120 | 20  0  60  0  60   0 48 |  0 30  0 24  0 24  0 4 |  0 12  0 2  0 2 0 |  * 2 * *
x . x o3o5x   80 | 40  0 40 120 |  0 20  60  0   0  60 48 |  0  0 30 24  0  0 24 4 |  0  0 12 2  0 0 2 |  * * 2 *
. x x o3o5x   80 |  0 40 40 120 |  0  0   0 20  60  60 48 |  0  0  0  0 30 24 24 4 |  0  0  0 0 12 2 2 |  * * * 2

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