Acronym penhix
Name pentachoron - hexateron duoprism,
vertex figure of teru
Circumradius 7/sqrt(60) = 0.903696
Face vector 30, 135, 310, 455, 461, 330, 165, 55, 11
Confer
general polytopal classes:
Wythoffian polyyotta   segmentoyotta   lace simplices  

Incidence matrix according to Dynkin symbol

x3o3o3o x3o3o3o3o

. . . . . . . . . | 30 |  4  5 |  6  20  10 |  4  30  40 10 | 1 20  60  40  5 |  5  40  60 20 1 | 10 40 30  4 | 10 20  6 | 5 4
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x . . . . . . . . |  2 | 60  * |  3   5   0 |  3  15  10  0 | 1 15  30  10  0 |  5  30  30  5 0 | 10 30 15  1 | 10 15  3 | 5 3
. . . . x . . . . |  2 |  * 75 |  0   4   4 |  0   6  16  6 | 0  4  24  24  4 |  1  16  36 16 1 |  4 24 24  4 |  6 16  6 | 4 4
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o . . . . . . . |  3 |  3  0 | 60   *   * |  2   5   0  0 | 1 10  10   0  0 |  5  20  10  0 0 | 10 20  5  0 | 10 10  1 | 5 2
x . . . x . . . . |  4 |  2  2 |  * 150   * |  0   3   4  0 | 0  3  12   6  0 |  1  12  18  4 0 |  4 18 12  1 |  6 12  3 | 4 3
. . . . x3o . . . |  3 |  0  3 |  *   * 100 |  0   0   4  3 | 0  0   6  12  3 |  0   4  18 12 1 |  1 12 18  4 |  3 12  6 | 3 4
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o3o . . . . . .   4 |  6  0 |  4   0   0 | 30   *   *  * | 1  5   0   0  0 |  5  10   0  0 0 | 10 10  0  0 | 10  5  0 | 5 1
x3o . . x . . . .   6 |  6  3 |  2   3   0 |  * 150   *  * | 0  2   4   0  0 |  1   8   6  0 0 |  4 12  4  0 |  6  8  1 | 4 2
x . . . x3o . . .   6 |  3  6 |  0   3   2 |  *   * 200  * | 0  0   3   3  0 |  0   3   9  3 0 |  1  9  9  1 |  3  9  3 | 3 3
. . . . x3o3o . .   4 |  0  6 |  0   0   4 |  *   *   * 75 | 0  0   0   4  2 |  0   0   6  8 1 |  0  4 12  4 |  1  8  6 | 2 4
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o3o3o . . . . .   5 | 10  0 | 10   0   0 |  5   0   0  0 | 6  *   *   *  *   5   0   0  0 0 | 10  0  0  0 | 10  0  0 | 5 0
x3o3o . x . . . .   8 | 12  4 |  8   6   0 |  2   4   0  0 | * 75   *   *  * |  1   4   0  0 0 |  4  6  0  0 |  6  4  0 | 4 1
x3o . . x3o . . .   9 |  9  9 |  3   9   3 |  0   3   3  0 | *  * 200   *  * |  0   2   3  0 0 |  1  6  3  0 |  3  6  1 | 3 2
x . . . x3o3o . .   8 |  4 12 |  0   6   8 |  0   0   4  2 | *  *   * 150  * |  0   0   3  2 0 |  0  3  6  1 |  1  6  3 | 2 3
. . . . x3o3o3o .   5 |  0 10 |  0   0  10 |  0   0   0  5 | *  *   *   * 30 |  0   0   0  4 1 |  0  0  6  4 |  0  4  6 | 1 4
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o3o3o x . . . .  10 | 20  5 | 20  10   0 | 10  10   0  0 | 2  5   0   0  0 | 15   *   *  * *   4  0  0  0 |  6  0  0 | 4 0
x3o3o . x3o . . .  12 | 18 12 | 12  18   4 |  3  12   6  0 | 0  3   4   0  0 |  * 100   *  * * |  1  3  0  0 |  3  3  0 | 3 1
x3o . . x3o3o . .  12 | 12 18 |  4  18  12 |  0   6  12  3 | 0  0   4   3  0 |  *   * 150  * * |  0  2  2  0 |  1  4  1 | 2 2
x . . . x3o3o3o .  10 |  5 20 |  0  10  20 |  0   0  10 10 | 0  0   0   5  2 |  *   *   * 60 * |  0  0  3  1 |  0  3  3 | 1 3
. . . . x3o3o3o3o   6 |  0 15 |  0   0  20 |  0   0   0 15 | 0  0   0   0  6 |  *   *   *  * 5   0  0  0  4 |  0  0  6 | 0 4
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o3o3o x3o . . .  15 | 30 15 | 30  30   5 | 15  30  10  0 | 3 15  10   0  0 |  3   5   0  0 0 | 20  *  *  * |  3  0  0 | 3 0
x3o3o . x3o3o . .  16 | 24 24 | 16  36  16 |  4  24  24  4 | 0  6  16   6  0 |  0   4   4  0 0 |  * 75  *  * |  1  2  0 | 2 1
x3o . . x3o3o3o .  15 | 15 30 |  5  30  30 |  0  10  30 15 | 0  0  10  15  3 |  0   0   5  3 0 |  *  * 60  * |  0  2  1 | 1 2
x . . . x3o3o3o3o  12 |  6 30 |  0  15  40 |  0   0  20 30 | 0  0   0  15 12 |  0   0   0  6 2 |  *  *  * 10 |  0  0  3 | 0 3
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o3o3o x3o3o . .  20 | 40 30 | 40  60  20 | 20  60  40  5 | 4 30  40  10  0 |  6  20  10  0 0 |  4  5  0  0 | 15  *  * | 2 0
x3o3o . x3o3o3o .  20 | 30 40 | 20  60  40 |  5  40  60 20 | 0 10  40  30  4 |  0  10  20  6 0 |  0  5  4  0 |  * 30  * | 1 1
x3o . . x3o3o3o3o  18 | 18 45 |  6  45  60 |  0  15  60 45 | 0  0  20  45 18 |  0   0  15 18 3 |  0  0  6  3 |  *  * 10 | 0 2
------------------+----+-------+------------+---------------+-----------------+-----------------+-------------+----------+----
x3o3o3o x3o3o3o .  25 | 50 50 | 50 100  50 | 25 100 100 25 | 5 50 100  50  5 | 10  50  50 10 0 | 10 25 10  0 |  5  5  0 | 6 *
x3o3o . x3o3o3o3o  24 | 36 60 | 24  90  80 |  6  60 120 60 | 0 15  80  90 24 |  0  20  60 36 4 |  0 15 24  6 |  0  6  4 | * 5

ox3oo3oo xx3oo3oo3oo3oo&#x   height = sqrt(5/8) = 0.790569
(hix || tethix)

...

xx3oo3oo3oo ox3oo3oo3oo&#x   height = sqrt(3/5) = 0.774597
(pen || pendip)

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