Acronym squike
Name square-icosahedron duoprism
Circumradius sqrt[(9+sqrt(5))/8] = 1.185120
Confer
more general:
n,ike-dip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x4o x3o5o

. . . . . | 48 |  2   5 |  1  10  5 |  5 10 1 |  5 2
----------+----+--------+-----------+---------+-----
x . . . . |  2 | 48   * |  1   5  0 |  5  5 0 |  5 1
. . x . . |  2 |  * 120 |  0   2  2 |  1  4 1 |  2 2
----------+----+--------+-----------+---------+-----
x4o . . . |  4 |  4   0 | 12   *  * |  5  0 0 |  5 0
x . x . . |  4 |  2   2 |  * 120  * |  1  2 0 |  2 1
. . x3o . |  3 |  0   3 |  *   * 80 |  0  2 1 |  1 2
----------+----+--------+-----------+---------+-----
x4o x . .   8 |  8   4 |  2   4  0 | 30  * * |  2 0
x . x3o .   6 |  3   6 |  0   3  2 |  * 80 * |  1 1
. . x3o5o  12 |  0  30 |  0   0 20 |  *  * 4 |  0 2
----------+----+--------+-----------+---------+-----
x4o x3o .  12 | 12  12 |  3  12  4 |  3  4 0 | 20 *
x . x3o5o  24 | 12  60 |  0  30 40 |  0 20 2 |  * 4

x x x3o5o

. . . . . | 48 |  1  1   5 |  1  5  5  5 |  5  5  5 1 |  5 1 1
----------+----+-----------+-------------+------------+-------
x . . . . |  2 | 24  *   * |  1  5  0  0 |  5  5  0 0 |  5 1 0
. x . . . |  2 |  * 24   * |  1  0  5  0 |  5  0  5 0 |  5 0 1
. . x . . |  2 |  *  * 120 |  0  1  1  2 |  1  2  2 1 |  2 1 1
----------+----+-----------+-------------+------------+-------
x x . . . |  4 |  2  2   0 | 12  *  *  * |  5  0  0 0 |  5 0 0
x . x . . |  4 |  2  0   2 |  * 60  *  * |  1  2  0 0 |  2 1 0
. x x . . |  4 |  0  2   2 |  *  * 60  * |  1  0  2 0 |  2 0 1
. . x3o . |  3 |  0  0   3 |  *  *  * 80 |  0  1  1 1 |  1 1 1
----------+----+-----------+-------------+------------+-------
x x x . .   8 |  4  4   4 |  2  2  2  0 | 30  *  * * |  2 0 0
x . x3o .   6 |  3  0   6 |  0  3  0  2 |  * 40  * * |  1 1 0
. x x3o .   6 |  0  3   6 |  0  0  3  2 |  *  * 40 * |  1 0 1
. . x3o5o  12 |  0  0  30 |  0  0  0 20 |  *  *  * 4 |  0 1 1
----------+----+-----------+-------------+------------+-------
x x x3o .  12 |  6  6  12 |  3  6  6  4 |  3  2  2 0 | 20 * *
x . x3o5o  24 | 12  0  60 |  0 30  0 40 |  0 20  0 2 |  * 2 *
. x x3o5o  24 |  0 12  60 |  0  0 30 40 |  0  0 20 2 |  * * 2

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