Acronym codoe
Name cuboctahedron-dodecahedron duoprism
Circumradius sqrt[(17+3 sqrt(5))/8] = 1.721489

Incidence matrix according to Dynkin symbol

o3x4o o3o5x

. . . . . . | 240 |   4   3 |   2   2  12   3 |  1   6   6  12  1 |  3  6  6  4 |  3 2 2
------------+-----+---------+-----------------+-------------------+-------------+-------
. x . . . . |   2 | 480   * |   1   1   3   0 |  1   3   3   3  0 |  3  3  3  1 |  3 1 1
. . . . . x |   2 |   * 360 |   0   0   4   2 |  0   2   2   8  1 |  1  4  4  4 |  2 2 2
------------+-----+---------+-----------------+-------------------+-------------+-------
o3x . . . . |   3 |   3   0 | 160   *   *   * |  1   3   0   0  0 |  3  3  0  0 |  3 1 0
. x4o . . . |   4 |   4   0 |   * 120   *   * |  1   0   3   0  0 |  3  0  3  0 |  3 0 1
. x . . . x |   4 |   2   2 |   *   * 720   * |  0   1   1   2  0 |  1  2  2  1 |  2 1 1
. . . . o5x |   5 |   0   5 |   *   *   * 144 |  0   0   0   4  1 |  0  2  2  4 |  1 2 2
------------+-----+---------+-----------------+-------------------+-------------+-------
o3x4o . . .   12 |  24   0 |   8   6   0   0 | 20   *   *   *  * |  3  0  0  0 |  3 0 0
o3x . . . x    6 |   6   3 |   2   0   3   0 |  * 240   *   *  * |  1  2  0  0 |  2 1 0
. x4o . . x    8 |   8   4 |   0   2   4   0 |  *   * 180   *  * |  1  0  2  0 |  2 0 1
. x . . o5x   10 |   5  10 |   0   0   5   2 |  *   *   * 288  * |  0  1  1  1 |  1 1 1
. . . o3o5x   20 |   0  30 |   0   0   0  12 |  *   *   *   * 12 |  0  0  0  4 |  0 2 2
------------+-----+---------+-----------------+-------------------+-------------+-------
o3x4o . . x   24 |  48  12 |  16  12  24   0 |  2   8   6   0  0 | 30  *  *  * |  2 0 0
o3x . . o5x   15 |  15  15 |   5   0  15   3 |  0   5   0   3  0 |  * 96  *  * |  1 1 0
. x4o . o5x   20 |  20  20 |   0   5  20   4 |  0   0   5   4  0 |  *  * 72  * |  1 0 1
. x . o3o5x   40 |  20  60 |   0   0  30  24 |  0   0   0  12  2 |  *  *  * 24 |  0 1 1
------------+-----+---------+-----------------+-------------------+-------------+-------
o3x4o . o5x   60 | 120  60 |  40  30 120  12 |  5  40  30  24  0 |  5  8  6  0 | 12 * *
o3x . o3o5x   60 |  60  90 |  20   0  90  36 |  0  30   0  36  3 |  0 12  0  3 |  * 8 *
. x4o o3o5x   80 |  80 120 |   0  20 120  48 |  0   0  30  48  4 |  0  0 12  4 |  * * 6

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