Acronym hati
Name hexagon - truncated-icosahedron duoprism
Circumradius sqrt[(37+9 sqrt(5))/8] = 2.672186
Confer n,ti-dip (n=3)  

Incidence matrix according to Dynkin symbol

x6o x3x5o

. . . . . | 360 |   2   1   2 |  1   2   4   2  1 |  1  2   4  2 1 |  2  1 2
----------+-----+-------------+-------------------+----------------+--------
x . . . . |   2 | 360   *   * |  1   1   2   0  0 |  1  2   2  1 0 |  2  1 1
. . x . . |   2 |   * 180   * |  0   2   0   2  0 |  1  0   4  0 1 |  2  0 2
. . . x . |   2 |   *   * 360 |  0   0   2   1  1 |  0  1   2  2 1 |  1  1 2
----------+-----+-------------+-------------------+----------------+--------
x6o . . . |   6 |   6   0   0 | 60   *   *   *  * |  1  2   0  0 0 |  2  1 0
x . x . . |   4 |   2   2   0 |  * 180   *   *  * |  1  0   2  0 0 |  2  0 1
x . . x . |   4 |   2   0   2 |  *   * 360   *  * |  0  1   1  1 0 |  1  1 1
. . x3x . |   6 |   0   3   3 |  *   *   * 120  * |  0  0   2  0 1 |  1  0 2
. . . x5o |   5 |   0   0   5 |  *   *   *   * 72 |  0  0   0  2 1 |  0  1 2
----------+-----+-------------+-------------------+----------------+--------
x6o x . .   12 |  12   6   0 |  2   6   0   0  0 | 30  *   *  * * |  2  0 0
x6o . x .   12 |  12   0   6 |  2   0   6   0  0 |  * 60   *  * * |  1  1 0
x . x3x .   12 |   6   6   6 |  0   3   3   2  0 |  *  * 120  * * |  1  0 1
x . . x5o   10 |   5   0  10 |  0   0   5   0  2 |  *  *   * 72 * |  0  1 1
. . x3x5o   60 |   0  30  60 |  0   0   0  20 12 |  *  *   *  * 6 |  0  0 2
----------+-----+-------------+-------------------+----------------+--------
x6o x3x .   36 |  36  18  18 |  6  18  18   6  0 |  3  3   6  0 0 | 20  * *
x6o . x5o   30 |  30   0  30 |  5   0  30   0  6 |  0  5   0  6 0 |  * 12 *
x . x3x5o  120 |  60  60 120 |  0  30  60  40 24 |  0  0  20 12 2 |  *  * 6

x3x x3x5o

. . . . . | 360 |   1   1   1   2 |  1  1   2  1   2   2  1 |  1  2  2  1  2  1 1 |  2  1 1 1
----------+-----+-----------------+-------------------------+---------------------+----------
x . . . . |   2 | 180   *   *   * |  1  1   2  0   0   0  0 |  1  2  2  1  0  0 0 |  2  1 1 0
. x . . . |   2 |   * 180   *   * |  1  0   0  1   2   0  0 |  1  2  0  0  2  1 0 |  2  1 0 1
. . x . . |   2 |   *   * 180   * |  0  1   0  1   0   2  0 |  1  0  2  0  2  0 1 |  2  0 1 1
. . . x . |   2 |   *   *   * 360 |  0  0   1  0   1   1  1 |  0  1  1  1  1  1 1 |  1  1 1 1
----------+-----+-----------------+-------------------------+---------------------+----------
x3x . . . |   6 |   3   3   0   0 | 60  *   *  *   *   *  * |  1  2  0  0  0  0 0 |  2  1 0 0
x . x . . |   4 |   2   0   2   0 |  * 90   *  *   *   *  * |  1  0  2  0  0  0 0 |  2  0 1 0
x . . x . |   4 |   2   0   0   2 |  *  * 180  *   *   *  * |  0  1  1  1  0  0 0 |  1  1 1 0
. x x . . |   4 |   0   2   2   0 |  *  *   * 90   *   *  * |  1  0  0  0  2  0 0 |  2  0 0 1
. x . x . |   4 |   0   2   0   2 |  *  *   *  * 180   *  * |  0  1  0  0  1  1 0 |  1  1 0 1
. . x3x . |   6 |   0   0   3   3 |  *  *   *  *   * 120  * |  0  0  1  0  1  0 1 |  1  0 1 1
. . . x5o |   5 |   0   0   0   5 |  *  *   *  *   *   * 72 |  0  0  0  1  0  1 1 |  0  1 1 1
----------+-----+-----------------+-------------------------+---------------------+----------
x3x x . .   12 |   6   6   6   0 |  2  3   0  3   0   0  0 | 30  *  *  *  *  * * |  2  0 0 0
x3x . x .   12 |   6   6   0   6 |  2  0   3  0   3   0  0 |  * 60  *  *  *  * * |  1  1 0 0
x . x3x .   12 |   6   0   6   6 |  0  3   3  0   0   2  0 |  *  * 60  *  *  * * |  1  0 1 0
x . . x5o   10 |   5   0   0  10 |  0  0   5  0   0   0  2 |  *  *  * 36  *  * * |  0  1 1 0
. x x3x .   12 |   0   6   6   6 |  0  0   0  3   3   2  0 |  *  *  *  * 60  * * |  1  0 0 1
. x . x5o   10 |   0   5   0  10 |  0  0   0  0   5   0  2 |  *  *  *  *  * 36 * |  0  1 0 1
. . x3x5o   60 |   0   0  30  60 |  0  0   0  0   0  20 12 |  *  *  *  *  *  * 6 |  0  0 1 1
----------+-----+-----------------+-------------------------+---------------------+----------
x3x x3x .   36 |  18  18  18  18 |  6  9   9  9   9   6  0 |  3  3  3  0  3  0 0 | 20  * * *
x3x . x5o   30 |  15  15   0  30 |  5  0  15  0  15   0  6 |  0  5  0  3  0  3 0 |  * 12 * *
x . x3x5o  120 |  60   0  60 120 |  0 30  60  0   0  40 24 |  0  0 20 12  0  0 2 |  *  * 3 *
. x x3x5o  120 |   0  60  60 120 |  0  0   0 30  60  40 24 |  0  0  0  0 20 12 2 |  *  * * 3

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