Acronym traspid
Name triangle - small-prismated-pentachoron duoprism
Circumradius 2/sqrt(3) = 1.154701

Incidence matrix according to Dynkin symbol

x3o x3o3o3x

o3o o3o3o3o | 60 |  2  3  3 |  1  6  6  3  6  3 |  3  3  6 12  6  1  3  3  1 |  3  6  3  2  6  6  2 1 | 1  3  3 1 2
------------+----+----------+-------------------+----------------------------+------------------------+------------
x . . . . . |  2 | 60  *  * |  1  3  3  0  0  0 |  3  3  3  6  3  0  0  0  0 |  3  6  3  1  3  3  1 0 | 1  3  3 1 1
. . x . . . |  2 |  * 90  * |  0  2  0  2  2  0 |  1  0  4  4  0  1  2  1  0 |  2  2  0  2  4  2  0 1 | 1  2  1 0 2
. . . . . x |  2 |  *  * 90 |  0  0  2  0  2  2 |  0  1  0  4  4  0  1  2  1 |  0  2  2  0  2  4  2 1 | 0  1  2 1 2
------------+----+----------+-------------------+----------------------------+------------------------+------------
x3o . . . . |  3 |  3  0  0 | 20  *  *  *  *  * |  3  3  0  0  0  0  0  0  0 |  3  6  3  0  0  0  0 0 | 1  3  3 1 0
x . x . . . |  4 |  2  2  0 |  * 90  *  *  *  * |  1  0  2  2  0  0  0  0  0 |  2  2  0  1  2  1  0 0 | 1  2  1 0 1
x . . . . x |  4 |  2  0  2 |  *  * 90  *  *  * |  0  1  0  2  2  0  0  0  0 |  0  2  2  0  1  2  1 0 | 0  1  2 1 1
. . x3o . . |  3 |  0  3  0 |  *  *  * 60  *  * |  0  0  2  0  0  1  1  0  0 |  1  0  0  2  2  0  0 1 | 1  1  0 0 2
. . x . . x |  4 |  0  2  2 |  *  *  *  * 90  * |  0  0  0  2  0  0  1  1  0 |  0  1  0  0  2  2  0 1 | 0  1  1 0 2
. . . . o3x |  3 |  0  0  3 |  *  *  *  *  * 60 |  0  0  0  0  2  0  0  1  1 |  0  0  1  0  0  2  2 1 | 0  0  1 1 2
------------+----+----------+-------------------+----------------------------+------------------------+------------
x3o x . . .   6 |  6  3  0 |  2  3  0  0  0  0 | 30  *  *  *  *  *  *  *  * |  2  2  0  0  0  0  0 0 | 1  2  1 0 0
x3o . . . x   6 |  6  0  3 |  2  0  3  0  0  0 |  * 30  *  *  *  *  *  *  * |  0  2  2  0  0  0  0 0 | 0  1  2 1 0
x . x3o . .   6 |  3  6  0 |  0  3  0  2  0  0 |  *  * 60  *  *  *  *  *  * |  1  0  0  1  1  0  0 0 | 1  1  0 0 1
x . x . . x   8 |  4  4  4 |  0  2  2  0  2  0 |  *  *  * 90  *  *  *  *  * |  0  1  0  0  1  1  0 0 | 0  1  1 0 1
x . . . o3x   6 |  3  0  6 |  0  0  3  0  0  2 |  *  *  *  * 60  *  *  *  * |  0  0  1  0  0  1  1 0 | 0  0  1 1 1
. . x3o3o .   4 |  0  6  0 |  0  0  0  4  0  0 |  *  *  *  *  * 15  *  *  * |  0  0  0  2  0  0  0 1 | 1  0  0 0 2
. . x3o . x   6 |  0  6  3 |  0  0  0  2  3  0 |  *  *  *  *  *  * 30  *  * |  0  0  0  0  2  0  0 1 | 0  1  0 0 2
. . x . o3x   6 |  0  3  6 |  0  0  0  0  3  2 |  *  *  *  *  *  *  * 30  * |  0  0  0  0  0  2  0 1 | 0  0  1 0 2
. . . o3o3x   4 |  0  0  6 |  0  0  0  0  0  4 |  *  *  *  *  *  *  *  * 15 |  0  0  0  0  0  0  2 1 | 0  0  0 1 2
------------+----+----------+-------------------+----------------------------+------------------------+------------
x3o x3o . .   9 |  9  9  0 |  3  9  0  3  0  0 |  3  0  3  0  0  0  0  0  0 | 20  *  *  *  *  *  * * | 1  1  0 0 0
x3o x . . x  12 | 12  6  6 |  4  6  6  0  3  0 |  2  2  0  3  0  0  0  0  0 |  * 30  *  *  *  *  * * | 0  1  1 0 0
x3o . . o3x   9 |  9  0  9 |  3  0  9  0  0  3 |  0  3  0  0  3  0  0  0  0 |  *  * 20  *  *  *  * * | 0  0  1 1 0
x . x3o3o .   8 |  4 12  0 |  0  6  0  8  0  0 |  0  0  4  0  0  2  0  0  0 |  *  *  * 15  *  *  * * | 1  0  0 0 1
x . x3o . x  12 |  6 12  6 |  0  6  3  4  6  0 |  0  0  2  3  0  0  2  0  0 |  *  *  *  * 30  *  * * | 0  1  0 0 1
x . x . o3x  12 |  6  6 12 |  0  3  6  0  6  4 |  0  0  0  3  2  0  0  2  0 |  *  *  *  *  * 30  * * | 0  0  1 0 1
x . . o3o3x   8 |  4  0 12 |  0  0  6  0  0  8 |  0  0  0  0  4  0  0  0  2 |  *  *  *  *  *  * 15 * | 0  0  0 1 1
. . x3o3o3x  20 |  0 30 30 |  0  0  0 20 30 20 |  0  0  0  0  0  5 10 10  5 |  *  *  *  *  *  *  * 3 | 0  0  0 0 2
------------+----+----------+-------------------+----------------------------+------------------------+------------
x3o x3o3o .  12 | 12 18  0 |  4 18  0 12  0  0 |  6  0 12  0  0  3  0  0  0 |  4  0  0  3  0  0  0 0 | 5  *  * * *
x3o x3o . x  18 | 18 18  9 |  6 18  9  6  9  0 |  6  3  6  9  0  0  3  0  0 |  2  3  0  0  3  0  0 0 | * 10  * * *
x3o x . o3x  18 | 18  9 18 |  6  9 18  0  9  6 |  3  6  0  9  6  0  0  3  0 |  0  3  2  0  0  3  0 0 | *  * 10 * *
x3o . o3o3x  12 | 12  0 18 |  4  0 18  0  0 12 |  0  6  0  0 12  0  0  0  3 |  0  0  4  0  0  0  3 0 | *  *  * 5 *
x . x3o3o3x  40 | 20 60 60 |  0 30 30 40 60 40 |  0  0 20 30 20 10 20 20 10 |  0  0  0  5 10 10  5 2 | *  *  * * 3
or
o3o o3o3o3o    | 60 |  2   6 |  1  12   6  6 |  6  12 12  2  6 |  6  6  4 12 1 |  2  6 2
---------------+----+--------+---------------+-----------------+---------------+--------
x . . . . .    |  2 | 60   * |  1   6   0  0 |  6   6  6  0  0 |  6  6  2  6 0 |  2  6 1
. . x . . .  & |  2 |  * 180 |  0   2   2  2 |  1   4  4  1  3 |  2  2  2  6 1 |  1  3 2
---------------+----+--------+---------------+-----------------+---------------+--------
x3o . . . .    |  3 |  3   0 | 20   *   *  * |  6   0  0  0  0 |  6  6  0  0 0 |  2  6 0
x . x . . .  & |  4 |  2   2 |  * 180   *  * |  1   2  2  0  0 |  2  2  1  3 0 |  1  3 1
. . x3o . .  & |  3 |  0   3 |  *   * 120  * |  0   2  0  1  1 |  1  0  2  2 1 |  1  1 2
. . x . . x    |  4 |  0   4 |  *   *   * 90 |  0   0  2  0  2 |  0  1  0  4 1 |  0  2 2
---------------+----+--------+---------------+-----------------+---------------+--------
x3o x . . .  &   6 |  6   3 |  2   3   0  0 | 60   *  *  *  * |  2  2  0  0 0 |  1  3 0
x . x3o . .  &   6 |  3   6 |  0   3   2  0 |  * 120  *  *  * |  1  0  1  1 0 |  1  1 1
x . x . . x      8 |  4   8 |  0   4   0  2 |  *   * 90  *  * |  0  1  0  2 0 |  0  2 1
. . x3o3o .  &   4 |  0   6 |  0   0   4  0 |  *   *  * 30  * |  0  0  2  0 1 |  1  0 2
. . x3o . x  &   6 |  0   9 |  0   0   2  3 |  *   *  *  * 60 |  0  0  0  2 1 |  0  1 2
---------------+----+--------+---------------+-----------------+---------------+--------
x3o x3o . .  &   9 |  9   9 |  3   9   3  0 |  3   3  0  0  0 | 40  *  *  * * |  1  1 0
x3o x . . x     12 | 12  12 |  4  12   0  3 |  4   0  3  0  0 |  * 30  *  * * |  0  2 0
x . x3o3o .  &   8 |  4  12 |  0   6   8  0 |  0   4  0  2  0 |  *  * 30  * * |  1  0 1
x . x3o . x  &  12 |  6  18 |  0   9   4  6 |  0   2  3  0  2 |  *  *  * 60 * |  0  1 1
. . x3o3o3x     20 |  0  60 |  0   0  40 30 |  0   0  0 10 20 |  *  *  *  * 3 |  0  0 2
---------------+----+--------+---------------+-----------------+---------------+--------
x3o x3o3o .  &  12 | 12  18 |  4  18  12  0 |  6  12  0  3  0 |  4  0  3  0 0 | 10  * *
x3o x3o . x  &  18 | 18  27 |  6  27   6  9 |  9   6  9  0  3 |  2  3  0  3 0 |  * 20 *
x . x3o3o3x     40 | 20 120 |  0  60  80 60 |  0  40 30 20 40 |  0  0 10 20 2 |  *  * 3

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