Acronym squati
Name square - truncated-icosahedron duoprism
Circumradius sqrt[(33+9 sqrt(5))/8] = 2.576932
Confer
more general:
n,ti-dip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x4o x3x5o

. . . . . | 240 |   2   1   2 |  1   2   4  2  1 |  1  2  4  2 1 |  2  1 2
----------+-----+-------------+------------------+---------------+--------
x . . . . |   2 | 240   *   * |  1   1   2  0  0 |  1  2  2  1 0 |  2  1 1
. . x . . |   2 |   * 120   * |  0   2   0  2  0 |  1  0  4  0 1 |  2  0 2
. . . x . |   2 |   *   * 240 |  0   0   2  1  1 |  0  1  2  2 1 |  1  1 2
----------+-----+-------------+------------------+---------------+--------
x4o . . . |   4 |   4   0   0 | 60   *   *  *  * |  1  2  0  0 0 |  2  1 0
x . x . . |   4 |   2   2   0 |  * 120   *  *  * |  1  0  2  0 0 |  2  0 1
x . . x . |   4 |   2   0   2 |  *   * 240  *  * |  0  1  1  1 0 |  1  1 1
. . x3x . |   6 |   0   3   3 |  *   *   * 80  * |  0  0  2  0 1 |  1  0 2
. . . x5o |   5 |   0   0   5 |  *   *   *  * 48 |  0  0  0  2 1 |  0  1 2
----------+-----+-------------+------------------+---------------+--------
x4o x . .    8 |   8   4   0 |  2   4   0  0  0 | 30  *  *  * * |  2  0 0
x4o . x .    8 |   8   0   4 |  2   0   4  0  0 |  * 60  *  * * |  1  1 0
x . x3x .   12 |   6   6   6 |  0   3   3  2  0 |  *  * 80  * * |  1  0 1
x . . x5o   10 |   5   0  10 |  0   0   5  0  2 |  *  *  * 48 * |  0  1 1
. . x3x5o   60 |   0  30  60 |  0   0   0 20 12 |  *  *  *  * 4 |  0  0 2
----------+-----+-------------+------------------+---------------+--------
x4o x3x .   24 |  24  12  12 |  6  12  12  4  0 |  3  3  4  0 0 | 20  * *
x4o . x5o   20 |  20   0  20 |  5   0  20  0  4 |  0  5  0  4 0 |  * 12 *
x . x3x5o  120 |  60  60 120 |  0  30  60 40 24 |  0  0 20 12 2 |  *  * 4

x x x3x5o

. . . . . | 240 |   1   1   1   2 |  1  1   2  1   2  2  1 |  1  2  2  1  2  1 1 |  2  1 1 1
----------+-----+-----------------+------------------------+---------------------+----------
x . . . . |   2 | 120   *   *   * |  1  1   2  0   0  0  0 |  1  2  2  1  0  0 0 |  2  1 1 0
. x . . . |   2 |   * 120   *   * |  1  0   0  1   2  0  0 |  1  2  0  0  2  1 0 |  2  1 0 1
. . x . . |   2 |   *   * 120   * |  0  1   0  1   0  2  0 |  1  0  2  0  2  0 1 |  2  0 1 1
. . . x . |   2 |   *   *   * 240 |  0  0   1  0   1  1  1 |  0  1  1  1  1  1 1 |  1  1 1 1
----------+-----+-----------------+------------------------+---------------------+----------
x x . . . |   4 |   2   2   0   0 | 60  *   *  *   *  *  * |  1  2  0  0  0  0 0 |  2  1 0 0
x . x . . |   4 |   2   0   2   0 |  * 60   *  *   *  *  * |  1  0  2  0  0  0 0 |  2  0 1 0
x . . x . |   4 |   2   0   0   2 |  *  * 120  *   *  *  * |  0  1  1  1  0  0 0 |  1  1 1 0
. x x . . |   4 |   0   2   2   0 |  *  *   * 60   *  *  * |  1  0  0  0  2  0 0 |  2  0 0 1
. x . x . |   4 |   0   2   0   2 |  *  *   *  * 120  *  * |  0  1  0  0  1  1 0 |  1  1 0 1
. . x3x . |   6 |   0   0   3   3 |  *  *   *  *   * 80  * |  0  0  1  0  1  0 1 |  1  0 1 1
. . . x5o |   5 |   0   0   0   5 |  *  *   *  *   *  * 48 |  0  0  0  1  0  1 1 |  0  1 1 1
----------+-----+-----------------+------------------------+---------------------+----------
x x x . .    8 |   4   4   4   0 |  2  2   0  2   0  0  0 | 30  *  *  *  *  * * |  2  0 0 0
x x . x .    8 |   4   4   0   4 |  2  0   2  0   2  0  0 |  * 60  *  *  *  * * |  1  1 0 0
x . x3x .   12 |   6   0   6   6 |  0  3   3  0   0  2  0 |  *  * 40  *  *  * * |  1  0 1 0
x . . x5o   10 |   5   0   0  10 |  0  0   5  0   0  0  2 |  *  *  * 24  *  * * |  0  1 1 0
. x x3x .   12 |   0   6   6   6 |  0  0   0  3   3  2  0 |  *  *  *  * 40  * * |  1  0 0 1
. x . x5o   10 |   0   5   0  10 |  0  0   0  0   5  0  2 |  *  *  *  *  * 24 * |  0  1 0 1
. . x3x5o   60 |   0   0  30  60 |  0  0   0  0   0 20 12 |  *  *  *  *  *  * 4 |  0  0 1 1
----------+-----+-----------------+------------------------+---------------------+----------
x x x3x .   24 |  12  12  12  12 |  6  6   6  6   6  4  0 |  3  3  2  0  2  0 0 | 20  * * *
x x . x5o   20 |  10  10   0  20 |  5  0  10  0  10  0  4 |  0  5  0  2  0  2 0 |  * 12 * *
x . x3x5o  120 |  60   0  60 120 |  0 30  60  0   0 40 24 |  0  0 20 12  0  0 2 |  *  * 2 *
. x x3x5o  120 |   0  60  60 120 |  0  0   0 30  60 40 24 |  0  0  0  0 20 12 2 |  *  * * 2

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