Acronym hike
Name hexagon icosahedron duoprism
Circumradius sqrt[(13+sqrt(5))/8] = 1.380039

Incidence matrix according to Dynkin symbol

x6o x3o5o

. . . . . | 72 |  2   5 |  1  10   5 |  5  10 1 |  5 2
----------+----+--------+------------+----------+-----
x . . . . |  2 | 72   * |  1   5   0 |  5   5 0 |  5 1
. . x . . |  2 |  * 180 |  0   2   2 |  1   4 1 |  2 2
----------+----+--------+------------+----------+-----
x6o . . . |  6 |  6   0 | 12   *   * |  5   0 0 |  5 0
x . x . . |  4 |  2   2 |  * 180   * |  1   2 0 |  2 1
. . x3o . |  3 |  0   3 |  *   * 120 |  0   2 1 |  1 2
----------+----+--------+------------+----------+-----
x6o x . .  12 | 12   6 |  2   6   0 | 30   * * |  2 0
x . x3o .   6 |  3   6 |  0   3   2 |  * 120 * |  1 1
. . x3o5o  12 |  0  30 |  0   0  20 |  *   * 6 |  0 2
----------+----+--------+------------+----------+-----
x6o x3o .  18 | 18  18 |  3  18   6 |  3   6 0 | 20 *
x . x3o5o  24 | 12  60 |  0  30  40 |  0  20 2 |  * 6

x3x x3o5o

. . . . . | 72 |  1  1   5 |  1  5  5   5 |  5  5  5 1 |  5 1 1
----------+----+-----------+--------------+------------+-------
x . . . . |  2 | 36  *   * |  1  5  0   0 |  5  5  0 0 |  5 1 0
. x . . . |  2 |  * 36   * |  1  0  5   0 |  5  0  5 0 |  5 0 1
. . x . . |  2 |  *  * 180 |  0  1  1   2 |  1  2  2 1 |  2 1 1
----------+----+-----------+--------------+------------+-------
x3x . . . |  6 |  3  3   0 | 12  *  *   * |  5  0  0 0 |  5 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
. . x3o . |  3 |  0  0   3 |  *  *  * 120 |  0  1  1 1 |  1 1 1
----------+----+-----------+--------------+------------+-------
x3x x . .  12 |  6  6   6 |  2  3  3   0 | 30  *  * * |  2 0 0
x . x3o .   6 |  3  0   6 |  0  3  0   2 |  * 60  * * |  1 1 0
. x x3o .   6 |  0  3   6 |  0  0  3   2 |  *  * 60 * |  1 0 1
. . x3o5o  12 |  0  0  30 |  0  0  0  20 |  *  *  * 6 |  0 1 1
----------+----+-----------+--------------+------------+-------
x3x x3o .  18 |  9  9  18 |  3  9  9   6 |  3  3  3 0 | 20 * *
x . x3o5o  24 | 12  0  60 |  0 30  0  40 |  0 20  0 2 |  * 3 *
. x x3o5o  24 |  0 12  60 |  0  0 30  40 |  0  0 20 2 |  * * 3

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