Acronym tetdoe
Name tetrahedron-dodecahedron duoprism
Circumradius sqrt[(12+3 sqrt(5))/8] = 1.529224

Incidence matrix according to Dynkin symbol

x3o3o o3o5x

. . . . . . | 80 |   3   3 |  3   9  3 |  1   9  9 1 |  3  9 3 |  3 3
------------+----+---------+-----------+-------------+---------+-----
x . . . . . |  2 | 120   * |  2   3  0 |  1   6  3 0 |  3  6 1 |  3 2
. . . . . x |  2 |   * 120 |  0   3  2 |  0   3  6 1 |  1  6 3 |  2 3
------------+----+---------+-----------+-------------+---------+-----
x3o . . . . |  3 |   3   0 | 80   *  * |  1   3  0 0 |  3  3 0 |  3 1
x . . . . x |  4 |   2   2 |  * 180  * |  0   2  2 0 |  1  4 1 |  2 2
. . . . o5x |  5 |   0   5 |  *   * 48 |  0   0  3 1 |  0  3 3 |  1 3
------------+----+---------+-----------+-------------+---------+-----
x3o3o . . .   4 |   6   0 |  4   0  0 | 20   *  * * |  3  0 0 |  3 0
x3o . . . x   6 |   6   3 |  2   3  0 |  * 120  * * |  1  2 0 |  2 1
x . . . o5x  10 |   5  10 |  0   5  2 |  *   * 72 * |  0  2 1 |  1 2
. . . o3o5x  20 |   0  30 |  0   0 12 |  *   *  * 4 |  0  0 3 |  0 3
------------+----+---------+-----------+-------------+---------+-----
x3o3o . . x   8 |  12   4 |  8   6  0 |  2   4  0 0 | 30  * * |  2 0
x3o . . o5x  15 |  15  15 |  5  15  3 |  0   5  3 0 |  * 48 * |  1 1
x . . o3o5x  40 |  20  60 |  0  30 24 |  0   0 12 2 |  *  * 6 |  0 2
------------+----+---------+-----------+-------------+---------+-----
x3o3o . o5x  20 |  30  20 | 20  30  4 |  5  20  6 0 |  5  4 0 | 12 *
x3o . o3o5x  60 |  60  90 | 20  90 36 |  0  30 36 3 |  0 12 3 |  * 4

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