Acronym tetid
Name tetrahedron-icosidodecahedron duoprism
Circumradius sqrt[(15+4 sqrt(5))/8] = 1.730039

Incidence matrix according to Dynkin symbol

x3o3o o3x5o

. . . . . . | 120 |   3   4 |   3  12  2  2 |  1  12   6  6 1 |  4  6  6 3 |  2  2 3
------------+-----+---------+---------------+-----------------+------------+--------
x . . . . . |   2 | 180   * |   2   4  0  0 |  1   8   2  2 0 |  4  4  4 1 |  2  2 2
. . . . x . |   2 |   * 240 |   0   3  1  1 |  0   3   3  3 1 |  1  3  3 3 |  1  1 3
------------+-----+---------+---------------+-----------------+------------+--------
x3o . . . . |   3 |   3   0 | 120   *  *  * |  1   4   0  0 0 |  4  2  2 0 |  2  2 1
x . . . x . |   4 |   2   2 |   * 360  *  * |  0   2   1  1 0 |  1  2  2 1 |  1  1 2
. . . o3x . |   3 |   0   3 |   *   * 80  * |  0   0   3  0 1 |  0  3  0 3 |  1  0 3
. . . . x5o |   5 |   0   5 |   *   *  * 48 |  0   0   0  3 1 |  0  0  3 3 |  0  1 3
------------+-----+---------+---------------+-----------------+------------+--------
x3o3o . . .    4 |   6   0 |   4   0  0  0 | 30   *   *  * * |  4  0  0 0 |  2  2 0
x3o . . x .    6 |   6   3 |   2   3  0  0 |  * 240   *  * * |  1  1  1 0 |  1  1 1
x . . o3x .    6 |   3   6 |   0   3  2  0 |  *   * 120  * * |  0  2  0 1 |  1  0 2
x . . . x5o   10 |   5  10 |   0   5  0  2 |  *   *   * 72 * |  0  0  2 1 |  0  1 2
. . . o3x5o   30 |   0  60 |   0   0 20 12 |  *   *   *  * 4 |  0  0  0 3 |  0  0 3
------------+-----+---------+---------------+-----------------+------------+--------
x3o3o . x .    8 |  12   4 |   8   6  0  0 |  2   4   0  0 0 | 60  *  * * |  1  1 0
x3o . o3x .    9 |   9   9 |   3   9  3  0 |  0   3   3  0 0 |  * 80  * * |  1  0 1
x3o . . x5o   15 |  15  15 |   5  15  0  3 |  0   5   0  3 0 |  *  * 48 * |  0  1 1
x . . o3x5o   60 |  30 120 |   0  60 40 24 |  0   0  20 12 2 |  *  *  * 6 |  0  0 2
------------+-----+---------+---------------+-----------------+------------+--------
x3o3o o3x .   12 |  18  12 |  12  18  4  0 |  3  12   6  0 0 |  3  4  0 0 | 20  * *
x3o3o . x5o   20 |  30  20 |  20  30  0  4 |  5  20   0  6 0 |  5  0  4 0 |  * 12 *
x3o . o3x5o   90 |  90 180 |  30 180 60 36 |  0  60  60 36 3 |  0 20 12 3 |  *  * 4

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