Acronym squagrid
Name square - great-rhombicosidodecahedron duoprism
Circumradius sqrt[33+12 sqrt(5)]/2 = 3.867584
Confer
more general:
n,grid-dip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x4o x3x5x

. . . . . | 480 |   2   1   1   1 |   1   2   2   2  1   1  1 |  1  1  1  2   2  2 1 |  1  1  1 2
----------+-----+-----------------+---------------------------+----------------------+-----------
x . . . . |   2 | 480   *   *   * |   1   1   1   1  0   0  0 |  1  1  1  1   1  1 0 |  1  1  1 1
. . x . . |   2 |   * 240   *   * |   0   2   0   0  1   1  0 |  1  0  0  2   2  0 1 |  1  1  0 2
. . . x . |   2 |   *   * 240   * |   0   0   2   0  1   0  1 |  0  1  0  2   0  2 1 |  1  0  1 2
. . . . x |   2 |   *   *   * 240 |   0   0   0   2  0   1  1 |  0  0  1  0   2  2 1 |  0  1  1 2
----------+-----+-----------------+---------------------------+----------------------+-----------
x4o . . . |   4 |   4   0   0   0 | 120   *   *   *  *   *  * |  1  1  1  0   0  0 0 |  1  1  1 0
x . x . . |   4 |   2   2   0   0 |   * 240   *   *  *   *  * |  1  0  0  1   1  0 0 |  1  1  0 1
x . . x . |   4 |   2   0   2   0 |   *   * 240   *  *   *  * |  0  1  0  1   0  1 0 |  1  0  1 1
x . . . x |   4 |   2   0   0   2 |   *   *   * 240  *   *  * |  0  0  1  0   1  1 0 |  0  1  1 1
. . x3x . |   6 |   0   3   3   0 |   *   *   *   * 80   *  * |  0  0  0  2   0  0 1 |  1  0  0 2
. . x . x |   4 |   0   2   0   2 |   *   *   *   *  * 120  * |  0  0  0  0   2  0 1 |  0  1  0 2
. . . x5x |  10 |   0   0   5   5 |   *   *   *   *  *   * 48 |  0  0  0  0   0  2 1 |  0  0  1 2
----------+-----+-----------------+---------------------------+----------------------+-----------
x4o x . .    8 |   8   4   0   0 |   2   4   0   0  0   0  0 | 60  *  *  *   *  * * |  1  1  0 0
x4o . x .    8 |   8   0   4   0 |   2   0   4   0  0   0  0 |  * 60  *  *   *  * * |  1  0  1 0
x4o . . x    8 |   8   0   0   4 |   2   0   0   4  0   0  0 |  *  * 60  *   *  * * |  0  1  1 0
x . x3x .   12 |   6   6   6   0 |   0   3   3   0  2   0  0 |  *  *  * 80   *  * * |  1  0  0 1
x . x . x    8 |   4   4   0   4 |   0   2   0   2  0   2  0 |  *  *  *  * 120  * * |  0  1  0 1
x . . x5x   20 |  10   0  10  10 |   0   0   5   5  0   0  2 |  *  *  *  *   * 48 * |  0  0  1 1
. . x3x5x  120 |   0  60  60  60 |   0   0   0   0 20  30 12 |  *  *  *  *   *  * 4 |  0  0  0 2
----------+-----+-----------------+---------------------------+----------------------+-----------
x4o x3x .   24 |  24  12  12   0 |   6  12  12   0  4   0  0 |  3  3  0  4   0  0 0 | 20  *  * *
x4o x . x   16 |  16   8   0   8 |   4   8   0   8  0   4  0 |  2  0  2  0   4  0 0 |  * 30  * *
x4o . x5x   40 |  40   0  20  20 |  10   0  20  20  0   0  4 |  0  5  5  0   0  4 0 |  *  * 12 *
x . x3x5x  240 | 120 120 120 120 |   0  60  60  60 40  60 24 |  0  0  0 20  30 12 2 |  *  *  * 4

snubbed forms: x4o s3s5s

x x x3x5x

. . . . . | 480 |   1   1   1   1   1 |   1   1   1   1   1   1   1  1   1  1 |  1  1  1  1  1  1  1  1  1 1 |  1  1  1 1 1
----------+-----+---------------------+---------------------------------------+------------------------------+-------------
x . . . . |   2 | 240   *   *   *   * |   1   1   1   1   0   0   0  0   0  0 |  1  1  1  1  1  1  0  0  0 0 |  1  1  1 1 0
. x . . . |   2 |   * 240   *   *   * |   1   0   0   0   1   1   1  0   0  0 |  1  1  1  0  0  0  1  1  1 0 |  1  1  1 0 1
. . x . . |   2 |   *   * 240   *   * |   0   1   0   0   1   0   0  1   1  0 |  1  0  0  1  1  0  1  1  0 1 |  1  1  0 1 1
. . . x . |   2 |   *   *   * 240   * |   0   0   1   0   0   1   0  1   0  1 |  0  1  0  1  0  1  1  0  1 1 |  1  0  1 1 1
. . . . x |   2 |   *   *   *   * 240 |   0   0   0   1   0   0   1  0   1  1 |  0  0  1  0  1  1  0  1  1 1 |  0  1  1 1 1
----------+-----+---------------------+---------------------------------------+------------------------------+-------------
x x . . . |   4 |   2   2   0   0   0 | 120   *   *   *   *   *   *  *   *  * |  1  1  1  0  0  0  0  0  0 0 |  1  1  1 0 0
x . x . . |   4 |   2   0   2   0   0 |   * 120   *   *   *   *   *  *   *  * |  1  0  0  1  1  0  0  0  0 0 |  1  1  0 1 0
x . . x . |   4 |   2   0   0   2   0 |   *   * 120   *   *   *   *  *   *  * |  0  1  0  1  0  1  0  0  0 0 |  1  0  1 1 0
x . . . x |   4 |   2   0   0   0   2 |   *   *   * 120   *   *   *  *   *  * |  0  0  1  0  1  1  0  0  0 0 |  0  1  1 1 0
. x x . . |   4 |   0   2   2   0   0 |   *   *   *   * 120   *   *  *   *  * |  1  0  0  0  0  0  1  1  0 0 |  1  1  0 0 1
. x . x . |   4 |   0   2   0   2   0 |   *   *   *   *   * 120   *  *   *  * |  0  1  0  0  0  0  1  0  1 0 |  1  0  1 0 1
. x . . x |   4 |   0   2   0   0   2 |   *   *   *   *   *   * 120  *   *  * |  0  0  1  0  0  0  0  1  1 0 |  0  1  1 0 1
. . x3x . |   6 |   0   0   3   3   0 |   *   *   *   *   *   *   * 80   *  * |  0  0  0  1  0  0  1  0  0 1 |  1  0  0 1 1
. . x . x |   4 |   0   0   2   0   2 |   *   *   *   *   *   *   *  * 120  * |  0  0  0  0  1  0  0  1  0 1 |  0  1  0 1 1
. . . x5x |  10 |   0   0   0   5   5 |   *   *   *   *   *   *   *  *   * 48 |  0  0  0  0  0  1  0  0  1 1 |  0  0  1 1 1
----------+-----+---------------------+---------------------------------------+------------------------------+-------------
x x x . .    8 |   4   4   4   0   0 |   2   2   0   0   2   0   0  0   0  0 | 60  *  *  *  *  *  *  *  * * |  1  1  0 0 0
x x . x .    8 |   4   4   0   4   0 |   2   0   2   0   0   2   0  0   0  0 |  * 60  *  *  *  *  *  *  * * |  1  0  1 0 0
x x . . x    8 |   4   4   0   0   4 |   2   0   0   2   0   0   2  0   0  0 |  *  * 60  *  *  *  *  *  * * |  0  1  1 0 0
x . x3x .   12 |   6   0   6   6   0 |   0   3   3   0   0   0   0  2   0  0 |  *  *  * 40  *  *  *  *  * * |  1  0  0 1 0
x . x . x    8 |   4   0   4   0   4 |   0   2   0   2   0   0   0  0   2  0 |  *  *  *  * 60  *  *  *  * * |  0  1  0 1 0
x . . x5x   20 |  10   0   0  10  10 |   0   0   5   5   0   0   0  0   0  2 |  *  *  *  *  * 24  *  *  * * |  0  0  1 1 0
. x x3x .   12 |   0   6   6   6   0 |   0   0   0   0   3   3   0  2   0  0 |  *  *  *  *  *  * 40  *  * * |  1  0  0 0 1
. x x . x    8 |   0   4   4   0   4 |   0   0   0   0   2   0   2  0   2  0 |  *  *  *  *  *  *  * 60  * * |  0  1  0 0 1
. x . x5x   20 |   0  10   0  10  10 |   0   0   0   0   0   5   5  0   0  2 |  *  *  *  *  *  *  *  * 24 * |  0  0  1 0 1
. . x3x5x  120 |   0   0  60  60  60 |   0   0   0   0   0   0   0 20  30 12 |  *  *  *  *  *  *  *  *  * 4 |  0  0  0 1 1
----------+-----+---------------------+---------------------------------------+------------------------------+-------------
x x x3x .   24 |  12  12  12  12   0 |   6   6   6   0   6   6   0  4   0  0 |  3  3  0  2  0  0  3  0  0 0 | 20  *  * * *
x x x . x   16 |   8   8   8   0   8 |   4   4   0   4   4   0   4  0   4  0 |  2  0  2  0  2  0  0  2  0 0 |  * 30  * * *
x x . x5x   40 |  20  20   0  20  20 |  10   0  10  10   0  10  10  0   0  4 |  0  5  5  0  0  2  0  0  2 0 |  *  * 12 * *
x . x3x5x  240 | 120   0 120 120 120 |   0  60  60  60   0   0   0 40  60 24 |  0  0  0 20 30 12  0  0  0 2 |  *  *  * 2 *
. x x3x5x  240 |   0 120 120 120 120 |   0   0   0   0  60  60  60 40  60 24 |  0  0  0  0  0  0 20 30 12 2 |  *  *  * * 2

snubbed forms: x x s3s5s

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