Acronym squarap
Name square - rectified-pentachoron duoprism
Circumradius sqrt(11/10) = 1.048809
Volume 11 sqrt(5)/96 = 0.256216
Face vector 40, 160, 250, 190, 74, 14
Confer
more general:
n,rap-dip  
general polytopal classes:
Wythoffian polypeta   lace simplices  

Incidence matrix according to Dynkin symbol

x4o o3x3o3o

. . . . . . | 40 |  2   6 |  1  12  3  6 |  6  6 12  3  2 |  3  6  6  4 1 | 3 2 2
------------+----+--------+--------------+----------------+---------------+------
x . . . . . |  2 | 40   * |  1   6  0  0 |  6  3  6  0  0 |  3  6  3  2 0 | 3 2 1
. . . x . . |  2 |  * 120 |  0   2  1  2 |  1  2  4  2  1 |  1  2  4  2 1 | 2 1 2
------------+----+--------+--------------+----------------+---------------+------
x4o . . . . |  4 |  4   0 | 10   *  *  *   6  0  0  0  0 |  3  6  0  0 0 | 3 2 0
x . . x . . |  4 |  2   2 |  * 120  *  * |  1  1  2  0  0 |  1  2  2  1 0 | 2 1 1
. . o3x . . |  3 |  0   3 |  *   * 40  * |  0  2  0  2  0 |  1  0  4  0 1 | 2 0 2
. . . x3o . |  3 |  0   3 |  *   *  * 80 |  0  0  2  1  1 |  0  1  2  2 1 | 1 1 2
------------+----+--------+--------------+----------------+---------------+------
x4o . x . .   8 |  8   4 |  2   4  0  0 | 30  *  *  *  * |  1  2  0  0 0 | 2 1 0
x . o3x . .   6 |  3   6 |  0   3  2  0 |  * 40  *  *  * |  1  0  2  0 0 | 2 0 1
x . . x3o .   6 |  3   6 |  0   3  0  2 |  *  * 80  *  * |  0  1  1  1 0 | 1 1 1
. . o3x3o .   6 |  0  12 |  0   0  4  4 |  *  *  * 20  * |  0  0  2  0 1 | 1 0 2
. . . x3o3o   4 |  0   6 |  0   0  0  4 |  *  *  *  * 20 |  0  0  0  2 1 | 0 1 2
------------+----+--------+--------------+----------------+---------------+------
x4o o3x . .  12 | 12  12 |  3  12  4  0 |  3  4  0  0  0 | 10  *  *  * * | 2 0 0
x4o . x3o .  12 | 12  12 |  3  12  0  4 |  3  0  4  0  0 |  * 20  *  * * | 1 1 0
x . o3x3o .  12 |  6  24 |  0  12  8  8 |  0  4  4  2  0 |  *  * 20  * * | 1 0 1
x . . x3o3o   8 |  4  12 |  0   6  0  8 |  0  0  4  0  2 |  *  *  * 20 * | 0 1 1
. . o3x3o3o  10 |  0  30 |  0   0 10 20 |  0  0  0  5  5 |  *  *  *  * 4 | 0 0 2
------------+----+--------+--------------+----------------+---------------+------
x4o o3x3o .  24 | 24  48 |  6  48 16 16 | 12 16 16  4  0 |  4  4  4  0 0 | 5 * *
x4o . x3o3o  16 | 16  24 |  4  24  0 16 |  6  0 16  0  4 |  0  4  0  4 0 | * 5 *
x . o3x3o3o  20 | 10  60 |  0  30 20 40 |  0 10 20 10 10 |  0  0  5  5 2 | * * 4

x x o3x3o3o

. . . . . . | 40 |  1  1   6 |  1  6  6  3  6 |  6  3  6  3  6  3  2 |  3  6  3  2  3  2 1 | 3 2 1 1
------------+----+-----------+----------------+----------------------+---------------------+--------
x . . . . . |  2 | 20  *   * |  1  6  0  0  0 |  6  3  6  0  0  0  0 |  3  6  3  2  0  0 0 | 3 2 1 0
. x . . . . |  2 |  * 20   * |  1  0  6  0  0 |  6  0  0  3  6  0  0 |  3  6  0  0  3  2 0 | 3 2 0 1
. . . x . . |  2 |  *  * 120 |  0  1  1  1  2 |  1  1  2  1  2  2  1 |  1  2  2  1  2  1 1 | 2 1 1 1
------------+----+-----------+----------------+----------------------+---------------------+--------
x x . . . . |  4 |  2  2   0 | 10  *  *  *  *   6  0  0  0  0  0  0 |  3  6  0  0  0  0 0 | 3 2 0 0
x . . x . . |  4 |  2  0   2 |  * 60  *  *  * |  1  1  2  0  0  0  0 |  1  2  2  1  0  0 0 | 2 1 1 0
. x . x . . |  4 |  0  2   2 |  *  * 60  *  * |  1  0  0  1  2  0  0 |  1  2  0  0  2  1 0 | 2 1 0 1
. . o3x . . |  3 |  0  0   3 |  *  *  * 40  * |  0  1  0  1  0  2  0 |  1  0  2  0  2  0 1 | 2 0 1 1
. . . x3o . |  3 |  0  0   3 |  *  *  *  * 80 |  0  0  1  0  1  1  1 |  0  1  1  1  1  1 1 | 1 1 1 1
------------+----+-----------+----------------+----------------------+---------------------+--------
x x . x . .   8 |  4  4   4 |  2  2  2  0  0 | 30  *  *  *  *  *  * |  1  2  0  0  0  0 0 | 2 1 0 0
x . o3x . .   6 |  3  0   6 |  0  3  0  2  0 |  * 20  *  *  *  *  * |  1  0  2  0  0  0 0 | 2 0 1 0
x . . x3o .   6 |  3  0   6 |  0  3  0  0  2 |  *  * 40  *  *  *  * |  0  1  1  1  0  0 0 | 1 1 1 0
. x o3x . .   6 |  0  3   6 |  0  0  3  2  0 |  *  *  * 20  *  *  * |  1  0  0  0  2  0 0 | 2 0 0 1
. x . x3o .   6 |  0  3   6 |  0  0  3  0  2 |  *  *  *  * 40  *  * |  0  1  0  0  1  1 0 | 1 1 0 1
. . o3x3o .   6 |  0  0  12 |  0  0  0  4  4 |  *  *  *  *  * 20  * |  0  0  1  0  1  0 1 | 1 0 1 1
. . . x3o3o   4 |  0  0   6 |  0  0  0  0  4 |  *  *  *  *  *  * 20 |  0  0  0  1  0  1 1 | 0 1 1 1
------------+----+-----------+----------------+----------------------+---------------------+--------
x x o3x . .  12 |  6  6  12 |  3  6  6  4  0 |  3  2  0  2  0  0  0 | 10  *  *  *  *  * * | 2 0 0 0
x x . x3o .  12 |  6  6  12 |  3  6  6  0  4 |  3  0  2  0  2  0  0 |  * 20  *  *  *  * * | 1 1 0 0
x . o3x3o .  12 |  6  0  24 |  0 12  0  8  8 |  0  4  4  0  0  2  0 |  *  * 10  *  *  * * | 1 0 1 0
x . . x3o3o   8 |  4  0  12 |  0  6  0  0  8 |  0  0  4  0  0  0  2 |  *  *  * 10  *  * * | 0 1 1 0
. x o3x3o .  12 |  0  6  24 |  0  0 12  8  8 |  0  0  0  4  4  2  0 |  *  *  *  * 10  * * | 1 0 0 1
. x . x3o3o   8 |  0  4  12 |  0  0  6  0  8 |  0  0  0  0  4  0  2 |  *  *  *  *  * 10 * | 0 1 0 1
. . o3x3o3o  10 |  0  0  30 |  0  0  0 10 20 |  0  0  0  0  0  5  5 |  *  *  *  *  *  * 4 | 0 0 1 1
------------+----+-----------+----------------+----------------------+---------------------+--------
x x o3x3o .  24 | 12 12  48 |  6 24 24 16 16 | 12  8  8  8  8  4  0 |  4  4  2  0  2  0 0 | 5 * * *
x x . x3o3o  16 |  8  8  24 |  4 12 12  0 16 |  6  0  8  0  8  0  4 |  0  4  0  2  0  2 0 | * 5 * *
x . o3x3o3o  20 | 10  0  60 |  0 30  0 20 40 |  0 10 20  0  0 10 10 |  0  0  5  5  0  0 2 | * * 2 *
. x o3x3o3o  20 |  0 10  60 |  0  0 30 20 40 |  0  0  0 10 20 10 10 |  0  0  0  0  5  5 2 | * * * 2

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