Acronym hadoe
Name hexagon - dodecahedron duoprism
Circumradius sqrt[(17+3 sqrt(5))/8] = 1.721489
Confer n,doe-dip  

Incidence matrix according to Dynkin symbol

x6o o3o5x

. . . . . | 120 |   2   3 |  1   6  3 |  3  6 1 |  3 2
----------+-----+---------+-----------+---------+-----
x . . . . |   2 | 120   * |  1   3  0 |  3  3 0 |  3 1
. . . . x |   2 |   * 180 |  0   2  2 |  1  4 1 |  2 2
----------+-----+---------+-----------+---------+-----
x6o . . . |   6 |   6   0 | 20   *  * |  3  0 0 |  3 0
x . . . x |   4 |   2   2 |  * 180  * |  1  2 0 |  2 1
. . . o5x |   5 |   0   5 |  *   * 72 |  0  2 1 |  1 2
----------+-----+---------+-----------+---------+-----
x6o . . x   12 |  12   6 |  2   6  0 | 30  * * |  2 0
x . . o5x   10 |   5  10 |  0   5  2 |  * 72 * |  1 1
. . o3o5x   20 |   0  30 |  0   0 12 |  *  * 6 |  0 2
----------+-----+---------+-----------+---------+-----
x6o . o5x   30 |  30  30 |  5  30  6 |  5  6 0 | 12 *
x . o3o5x   40 |  20  60 |  0  30 24 |  0 12 2 |  * 6

x3x o3o5x

. . . . . | 120 |  1  1   3 |  1  3  3  3 |  3  3  3 1 |  3 1 1
----------+-----+-----------+-------------+------------+-------
x . . . . |   2 | 60  *   * |  1  3  0  0 |  3  3  0 0 |  3 1 0
. x . . . |   2 |  * 60   * |  1  0  3  0 |  3  0  3 0 |  3 0 1
. . . . x |   2 |  *  * 180 |  0  1  1  2 |  1  2  2 1 |  2 1 1
----------+-----+-----------+-------------+------------+-------
x3x . . . |   6 |  3  3   0 | 20  *  *  * |  3  0  0 0 |  3 0 0
x . . . x |   4 |  2  0   2 |  * 90  *  * |  1  2  0 0 |  2 1 0
. x . . x |   4 |  0  2   2 |  *  * 90  * |  1  0  2 0 |  2 0 1
. . . o5x |   5 |  0  0   5 |  *  *  * 72 |  0  1  1 1 |  1 1 1
----------+-----+-----------+-------------+------------+-------
x3x . . x   12 |  6  6   6 |  2  3  3  0 | 30  *  * * |  2 0 0
x . . o5x   10 |  5  0  10 |  0  5  0  2 |  * 36  * * |  1 1 0
. x . o5x   10 |  0  5  10 |  0  0  5  2 |  *  * 36 * |  1 0 1
. . o3o5x   20 |  0  0  30 |  0  0  0 12 |  *  *  * 6 |  0 1 1
----------+-----+-----------+-------------+------------+-------
x3x . o5x   30 | 15 15  30 |  5 15 15  6 |  5  3  3 0 | 12 * *
x . o3o5x   40 | 20  0  60 |  0 30  0 24 |  0 12  0 2 |  * 3 *
. x o3o5x   40 |  0 20  60 |  0  0 30 24 |  0  0 12 2 |  * * 3

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