Acronym tetike
Name tetrahedron-icosahedron duoprism
Circumradius sqrt[sqrt(5)/8+1] = 1.131154

Incidence matrix according to Dynkin symbol

x3o3o x3o5o

. . . . . . | 48 |  3   5 |  3  15  5 |  1  15  15 1 |  5 15 3 |  5 3
------------+----+--------+-----------+--------------+---------+-----
x . . . . . |  2 | 72   * |  2   5  0 |  1  10   5 0 |  5 10 1 |  5 2
. . . x . . |  2 |  * 120 |  0   3  2 |  0   3   6 1 |  1  6 3 |  2 3
------------+----+--------+-----------+--------------+---------+-----
x3o . . . . |  3 |  3   0 | 48   *  * |  1   5   0 0 |  5  5 0 |  5 1
x . . x . . |  4 |  2   2 |  * 180  * |  0   2   2 0 |  1  4 1 |  2 2
. . . x3o . |  3 |  0   3 |  *   * 80 |  0   0   3 1 |  0  3 3 |  1 3
------------+----+--------+-----------+--------------+---------+-----
x3o3o . . .   4 |  6   0 |  4   0  0 | 12   *   * * |  5  0 0 |  5 0
x3o . x . .   6 |  6   3 |  2   3  0 |  * 120   * * |  1  2 0 |  2 1
x . . x3o .   6 |  3   6 |  0   3  2 |  *   * 120 * |  0  2 1 |  1 2
. . . x3o5o  12 |  0  30 |  0   0 20 |  *   *   * 4 |  0  0 3 |  0 3
------------+----+--------+-----------+--------------+---------+-----
x3o3o x . .   8 | 12   4 |  8   6  0 |  2   4   0 0 | 30  * * |  2 0
x3o . x3o .   9 |  9   9 |  3   9  3 |  0   3   3 0 |  * 80 * |  1 1
x . . x3o5o  24 | 12  60 |  0  30 40 |  0   0  20 2 |  *  * 6 |  0 2
------------+----+--------+-----------+--------------+---------+-----
x3o3o x3o .  12 | 18  12 | 12  18  4 |  3  12   6 0 |  3  4 0 | 20 *
x3o . x3o5o  36 | 36  90 | 12  90 60 |  0  30  60 3 |  0 20 3 |  * 4

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