Acronym ricope
Name rectified-icositetrachoron prism
Circumradius sqrt(13)/2 = 1.802776
Coordinates (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 1/2)   & all permutations in all but last coord., all changes of sign
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x o3x4o3o

. . . . . | 192 |  1   6 |   6   3   6 |  3   6  3  2 |  3  2 1
----------+-----+--------+-------------+--------------+--------
x . . . . |   2 | 96   *    6   0   0 |  3   6  0  0 |  3  2 0
. . x . . |   2 |  * 576 |   1   1   2 |  1   2  2  1 |  2  1 1
----------+-----+--------+-------------+--------------+--------
x . x . . |   4 |  2   2 | 288   *   * |  1   2  0  0 |  2  1 0
. o3x . . |   3 |  0   3 |   * 192   * |  1   0  2  0 |  2  0 1
. . x4o . |   4 |  0   4 |   *   * 288 |  0   1  1  1 |  1  1 1
----------+-----+--------+-------------+--------------+--------
x o3x . .    6 |  3   6 |   3   2   0 | 96   *  *  * |  2  0 0
x . x4o .    8 |  4   8 |   4   0   2 |  * 144  *  * |  1  1 0
. o3x4o .   12 |  0  24 |   0   8   6 |  *   * 48  * |  1  0 1
. . x4o3o    8 |  0  12 |   0   0   6 |  *   *  * 48 |  0  1 1
----------+-----+--------+-------------+--------------+--------
x o3x4o .   24 | 12  48 |  24  16  12 |  8   6  2  0 | 24  * *
x . x4o3o   16 |  8  24 |  12   0  12 |  0   6  0  2 |  * 24 *
. o3x4o3o   96 |  0 288 |   0  96 144 |  0   0 24 24 |  *  * 2

x x3o3x4o

. . . . . | 192 |  1   2   4 |  2   4  1   4   2  2 |  1  4  2  2  2  2  1 |  2  2 1 1
----------+-----+------------+----------------------+----------------------+----------
x . . . . |   2 | 96   *   *   2   4  0   0   0  0 |  1  4  2  2  0  0  0 |  2  2 1 0
. x . . . |   2 |  * 192   * |  1   0  1   2   0  0 |  1  2  0  0  2  1  0 |  2  1 0 1
. . . x . |   2 |  *   * 384 |  0   1  0   1   1  1 |  0  1  1  1  1  1  1 |  1  1 1 1
----------+-----+------------+----------------------+----------------------+----------
x x . . . |   4 |  2   2   0 | 96   *  *   *   *  * |  1  2  0  0  0  0  0 |  2  1 0 0
x . . x . |   4 |  2   0   2 |  * 192  *   *   *  * |  0  1  1  1  0  0  0 |  1  1 1 0
. x3o . . |   3 |  0   3   0 |  *   * 64   *   *  * |  1  0  0  0  2  0  0 |  2  0 0 1
. x . x . |   4 |  0   2   2 |  *   *  * 192   *  * |  0  1  0  0  1  1  0 |  1  1 0 1
. . o3x . |   3 |  0   0   3 |  *   *  *   * 128  * |  0  0  1  0  1  0  1 |  1  0 1 1
. . . x4o |   4 |  0   0   4 |  *   *  *   *   * 96 |  0  0  0  1  0  1  1 |  0  1 1 1
----------+-----+------------+----------------------+----------------------+----------
x x3o . .    6 |  3   6   0 |  3   0  2   0   0  0 | 32  *  *  *  *  *  * |  2  0 0 0
x x . x .    8 |  4   4   4 |  2   2  0   2   0  0 |  * 96  *  *  *  *  * |  1  1 0 0
x . o3x .    6 |  3   0   6 |  0   3  0   0   2  0 |  *  * 64  *  *  *  * |  1  0 1 0
x . . x4o    8 |  4   0   8 |  0   4  0   0   0  2 |  *  *  * 48  *  *  * |  0  1 1 0
. x3o3x .   12 |  0  12  12 |  0   0  4   6   4  0 |  *  *  *  * 32  *  * |  1  0 0 1
. x . x4o    8 |  0   4   8 |  0   0  0   4   0  2 |  *  *  *  *  * 48  * |  0  1 0 1
. . o3x4o   12 |  0   0  24 |  0   0  0   0   8  6 |  *  *  *  *  *  * 16 |  0  0 1 1
----------+-----+------------+----------------------+----------------------+----------
x x3o3x .   24 | 12  24  24 | 12  12  8  12   8  0 |  4  6  4  0  2  0  0 | 16  * * *
x x . x4o   16 |  8   8  16 |  4   8  0   8   0  4 |  0  4  0  2  0  2  0 |  * 24 * *
x . o3x4o   24 | 12   0  48 |  0  24  0   0  16 12 |  0  0  8  6  0  0  2 |  *  * 8 *
. x3o3x4o   96 |  0  96 192 |  0   0 32  96  64 48 |  0  0  0  0 16 24  8 |  *  * * 2

x x3o3x *c3x

. . . .    . | 192 |  1   2   2   2 |  2  2  2  1  2  2  1  1  2 |  1  2  2  1  1  2  1  1  2  1 | 1 1  2 1 1
-------------+-----+----------------+----------------------------+-------------------------------+-----------
x . . .    . |   2 | 96   *   *   *   2  2  2  0  0  0  0  0  0 |  1  2  2  1  1  2  0  0  0  0 | 1 1  2 1 0
. x . .    . |   2 |  * 192   *   * |  1  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 |  *   * 192   * |  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 |  *   *   * 192 |  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 | 96  *  *  *  *  *  *  *  * |  1  1  1  0  0  0  0  0  0  0 | 1 1  1 0 0
x . . x    . |   4 |  2   0   2   0 |  * 96  *  *  *  *  *  *  * |  0  1  0  1  0  1  0  0  0  0 | 1 0  1 1 0
x . . .    x |   4 |  2   0   0   2 |  *  * 96  *  *  *  *  *  * |  0  0  1  0  1  1  0  0  0  0 | 0 1  1 1 0
. x3o .    . |   3 |  0   3   0   0 |  *  *  * 64  *  *  *  *  * |  1  0  0  0  0  0  1  1  0  0 | 1 1  0 0 1
. x . x    . |   4 |  0   2   2   0 |  *  *  *  * 96  *  *  *  * |  0  1  0  0  0  0  1  0  1  0 | 1 0  1 0 1
. x . .    x |   4 |  0   2   0   2 |  *  *  *  *  * 96  *  *  * |  0  0  1  0  0  0  0  1  1  0 | 0 1  1 0 1
. . o3x    . |   3 |  0   0   3   0 |  *  *  *  *  *  * 64  *  * |  0  0  0  1  0  0  1  0  0  1 | 1 0  0 1 1
. . o . *c3x |   3 |  0   0   0   3 |  *  *  *  *  *  *  * 64  * |  0  0  0  0  1  0  0  1  0  1 | 0 1  0 1 1
. . . x    x |   4 |  0   0   2   2 |  *  *  *  *  *  *  *  * 96 |  0  0  0  0  0  1  0  0  1  1 | 0 0  1 1 1
-------------+-----+----------------+----------------------------+-------------------------------+-----------
x x3o .    .    6 |  3   6   0   0 |  3  0  0  2  0  0  0  0  0 | 32  *  *  *  *  *  *  *  *  * | 1 1  0 0 0
x x . x    .    8 |  4   4   4   0 |  2  2  0  0  2  0  0  0  0 |  * 48  *  *  *  *  *  *  *  * | 1 0  1 0 0
x x . .    x    8 |  4   4   0   4 |  2  0  2  0  0  2  0  0  0 |  *  * 48  *  *  *  *  *  *  * | 0 1  1 0 0
x . o3x    .    6 |  3   0   6   0 |  0  3  0  0  0  0  2  0  0 |  *  *  * 32  *  *  *  *  *  * | 1 0  0 1 0
x . o . *c3x    6 |  3   0   0   6 |  0  0  3  0  0  0  0  2  0 |  *  *  *  * 32  *  *  *  *  * | 0 1  0 1 0
x . . x    x    8 |  4   0   4   4 |  0  2  2  0  0  0  0  0  2 |  *  *  *  *  * 48  *  *  *  * | 0 0  1 1 0
. x3o3x    .   12 |  0  12  12   0 |  0  0  0  4  6  0  4  0  0 |  *  *  *  *  *  * 16  *  *  * | 1 0  0 0 1
. x3o . *c3x   12 |  0  12   0  12 |  0  0  0  4  0  6  0  4  0 |  *  *  *  *  *  *  * 16  *  * | 0 1  0 0 1
. x . x    x    8 |  0   4   4   4 |  0  0  0  0  2  2  0  0  2 |  *  *  *  *  *  *  *  * 48  * | 0 0  1 0 1
. . o3x *c3x   12 |  0   0  12  12 |  0  0  0  0  0  0  4  4  6 |  *  *  *  *  *  *  *  *  * 16 | 0 0  0 1 1
-------------+-----+----------------+----------------------------+-------------------------------+-----------
x x3o3x    .   24 | 12  24  24   0 | 12 12  0  8 12  0  8  0  0 |  4  6  0  4  0  0  2  0  0  0 | 8 *  * * *
x x3o . *c3x   24 | 12  24   0  24 | 12  0 12  8  0 12  0  8  0 |  4  0  6  0  4  0  0  2  0  0 | * 8  * * *
x x . x    x   16 |  8   8   8   8 |  4  4  4  0  4  4  0  0  4 |  0  2  2  0  0  2  0  0  2  0 | * * 24 * *
x . o3x *c3x   24 | 12   0  24  24 |  0 12 12  0  0  0  8  8 12 |  0  0  0  4  4  6  0  0  0  2 | * *  * 8 *
. x3o3x *c3x   96 |  0  96  96  96 |  0  0  0 32 48 48 32 32 48 |  0  0  0  0  0  0  8  8 24  8 | * *  * * 2

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