Acronym ratip
Name rectified-triacontiditeron prism
Circumradius sqrt(5)/2 = 1.118034
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign

Incidence matrix according to Dynkin symbol

x o3x3o3o4o

. . . . . . | 80 |  1  12 |  12   6  24 |  6  24  12  16 | 12  16  8  2 |  8  2 1
------------+----+--------+-------------+----------------+--------------+--------
x . . . . . |  2 | 40   *   12   0   0 |  6  24   0   0 | 12  16  0  0 |  8  2 0
. . x . . . |  2 |  * 480 |   1   1   4 |  1   4   4   4 |  4   4  4  1 |  4  1 1
------------+----+--------+-------------+----------------+--------------+--------
x . x . . . |  4 |  2   2 | 240   *   * |  1   4   0   0 |  4   4  0  0 |  4  1 0
. o3x . . . |  3 |  0   3 |   * 160   * |  1   0   4   0 |  4   0  4  0 |  4  0 1
. . x3o . . |  3 |  0   3 |   *   * 640 |  0   1   1   2 |  1   2  2  1 |  2  1 1
------------+----+--------+-------------+----------------+--------------+--------
x o3x . . .   6 |  3   6 |   3   2   0 | 80   *   *   * |  4   0  0  0 |  4  0 0
x . x3o . .   6 |  3   6 |   3   0   2 |  * 320   *   * |  1   2  0  0 |  2  1 0
. o3x3o . .   6 |  0  12 |   0   4   4 |  *   * 160   * |  1   0  2  0 |  2  0 1
. . x3o3o .   4 |  0   6 |   0   0   4 |  *   *   * 320 |  0   1  1  1 |  1  1 1
------------+----+--------+-------------+----------------+--------------+--------
x o3x3o . .  12 |  6  24 |  12   8   8 |  4   4   2   0 | 80   *  *  * |  2  0 0
x . x3o3o .   8 |  4  12 |   6   0   8 |  0   4   0   2 |  * 160  *  * |  1  1 0
. o3x3o3o .  10 |  0  30 |   0  10  20 |  0   0   5   5 |  *   * 64  * |  1  0 1
. . x3o3o4o   8 |  0  24 |   0   0  32 |  0   0   0  16 |  *   *  * 20 |  0  1 1
------------+----+--------+-------------+----------------+--------------+--------
x o3x3o3o .  20 | 10  60 |  30  20  40 | 10  20  10  10 |  5   5  2  0 | 32  * *
x . x3o3o4o  16 |  8  48 |  24   0  64 |  0  32   0  32 |  0  16  0  2 |  * 10 *
. o3x3o3o4o  40 |  0 240 |   0  80 320 |  0   0  80 160 |  0   0 32 10 |  *  * 2

x o3o3o *c3x3o

. . . .    . . | 80 |  1  12 |  12  24   6 |  24  6   8   8  12 |  8  8 12  2  4  4 |  2  4  4 1
---------------+----+--------+-------------+--------------------+-------------------+-----------
x . . .    . . |  2 | 40   *   12   0   0 |  24  6   0   0   0 |  8  8 12  0  0  0 |  2  4  4 0
. . . .    x . |  2 |  * 480 |   1   4   1 |   4  1   2   2   4 |  2  2  4  1  2  2 |  1  2  2 1
---------------+----+--------+-------------+--------------------+-------------------+-----------
x . . .    x . |  4 |  2   2 | 240   *   * |   4  1   0   0   0 |  2  2  4  0  0  0 |  1  2  2 0
. . o . *c3x . |  3 |  0   3 |   * 640   * |   1  0   1   1   1 |  1  1  1  1  1  1 |  1  1  1 1
. . . .    x3o |  3 |  0   2 |   *   * 160 |   0  1   0   0   4 |  0  0  4  0  2  2 |  0  2  2 1
---------------+----+--------+-------------+--------------------+-------------------+-----------
x . o . *c3x .   6 |  3   6 |   3   2   0 | 320  *   *   *   * |  1  1  1  0  0  0 |  1  1  1 0
x . . .    x3o   6 |  3   6 |   3   0   2 |   * 80   *   *   * |  0  0  4  0  0  0 |  0  2  2 0
. o3o . *c3x .   4 |  0   6 |   0   4   0 |   *  * 160   *   * |  1  0  0  1  1  0 |  1  1  0 1
. . o3o *c3x .   4 |  0   6 |   0   4   0 |   *  *   * 160   * |  0  1  0  1  0  1 |  1  0  1 1
. . o . *c3x3o   6 |  0  12 |   0   4   4 |   *  *   *   * 160 |  0  0  1  0  1  1 |  0  1  1 1
---------------+----+--------+-------------+--------------------+-------------------+-----------
x o3o . *c3x .   8 |  4  12 |   6   8   0 |   4  0   2   0   0 | 80  *  *  *  *  * |  1  1  0 0
x . o3o *c3x .   8 |  4  12 |   6   8   0 |   4  0   0   2   0 |  * 80  *  *  *  * |  1  0  1 0
x . o . *c3x3o  12 |  6  24 |  12   8   8 |   4  4   0   0   2 |  *  * 80  *  *  * |  0  1  1 0
. o3o3o *c3x .   8 |  0  24 |   0  32   0 |   0  0   8   8   0 |  *  *  * 20  *  * |  1  0  0 1
. o3o . *c3x3o  10 |  0  30 |   0  20  10 |   0  0   5   0   5 |  *  *  *  * 32  * |  0  1  0 1
. . o3o *c3x3o  10 |  0  30 |   0  20  10 |   0  0   0   5   5 |  *  *  *  *  * 32 |  0  0  1 1
---------------+----+--------+-------------+--------------------+-------------------+-----------
x o3o3o *c3x .  16 |  8  48 |  24  64   0 |  32  0  16  16   0 |  8  8  0  2  0  0 | 10  *  * *
x o3o . *c3x3o  20 | 10  60 |  30  40  20 |  20 10  10   0  10 |  5  0  5  0  2  0 |  * 16  * *
x . o3o *c3x3o  20 | 10  60 |  30  40  20 |  20 10   0  10  10 |  0  5  5  0  0  2 |  *  * 16 *
. o3o3o *c3x3o  40 |  0 240 |   0 320  80 |   0  0  80  80  80 |  0  0  0 10 16 16 |  *  *  * 2

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