Acronym ikedoe
Name icosahedron-dodecahedron duoprism
Circumradius sqrt[7+2 sqrt(5)]/2 = 1.693527

Incidence matrix according to Dynkin symbol

x3o5o o3o5x

. . . . . . | 240 |   5   3 |   5  15   3 |  1  15  15  1 |  3  15  5 |  3  5
------------+-----+---------+-------------+---------------+-----------+------
x . . . . . |   2 | 600   * |   2   3   0 |  1   6   3  0 |  3   6  1 |  3  2
. . . . . x |   2 |   * 360 |   0   5   2 |  0   5  10  1 |  1  10  5 |  2  5
------------+-----+---------+-------------+---------------+-----------+------
x3o . . . . |   3 |   3   0 | 400   *   * |  1   3   0  0 |  3   3  0 |  3  1
x . . . . x |   4 |   2   2 |   * 900   * |  0   2   2  0 |  1   4  1 |  2  2
. . . . o5x |   5 |   0   5 |   *   * 144 |  0   0   5  1 |  0   5  5 |  1  5
------------+-----+---------+-------------+---------------+-----------+------
x3o5o . . .   12 |  30   0 |  20   0   0 | 20   *   *  * |  3   0  0 |  3  0
x3o . . . x    6 |   6   3 |   2   3   0 |  * 600   *  * |  1   2  0 |  2  1
x . . . o5x   10 |   5  10 |   0   5   2 |  *   * 360  * |  0   2  1 |  1  2
. . . o3o5x   20 |   0  30 |   0   0  12 |  *   *   * 12 |  0   0  5 |  0  5
------------+-----+---------+-------------+---------------+-----------+------
x3o5o . . x   24 |  60  12 |  40  30   0 |  2  20   0  0 | 30   *  * |  2  0
x3o . . o5x   15 |  15  15 |   5  15   3 |  0   5   3  0 |  * 240  * |  1  1
x . . o3o5x   40 |  20  60 |   0  30  24 |  0   0  12  2 |  *   * 30 |  0  2
------------+-----+---------+-------------+---------------+-----------+------
x3o5o . o5x   60 | 150  60 | 100 150  12 |  5 100  30  0 |  5  20  0 | 12  *
x3o . o3o5x   60 |  60  90 |  20  90  36 |  0  30  36  3 |  0  12  3 |  * 20

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