Acronym pendip
Name pentachoron duoprism,
vertex figure of icoy
Circumradius sqrt(10)/3 = 1.054093

Incidence matrix according to Dynkin symbol

x3o3o3o x3o3o3o

. . . . . . . . | 25 |  4  4 |  6  16  6 |  4  24  24  4 | 1 16  36 16 1 |  4 24 24  4 |  6 16  6 | 4 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x . . . . . . . |  2 | 50  * |  3   4  0 |  3  12   6  0 | 1 12  18  4 0 |  4 18 12  1 |  6 12  3 | 4 3
. . . . x . . . |  2 |  * 50 |  0   4  3 |  0   6  12  3 | 0  4  18 12 1 |  1 12 18  4 |  3 12  6 | 3 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o . . . . . . |  3 |  3  0 | 50   *  * |  2   4   0  0 | 1  8   6  0 0 |  4 12  4  0 |  6  8  1 | 4 2
x . . . x . . . |  4 |  2  2 |  * 100  * |  0   3   3  0 | 0  3   9  3 0 |  1  9  9  1 |  3  9  3 | 3 3
. . . . x3o . . |  3 |  0  3 |  *   * 50 |  0   0   4  2 | 0  0   6  8 1 |  0  4 12  4 |  1  8  6 | 2 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o . . . . .   4 |  6  0 |  4   0  0 | 25   *   *  * | 1  4   0  0 0 |  6  4  0  0 |  6  4  0 | 4 1
x3o . . x . . .   6 |  6  3 |  2   3  0 |  * 100   *  * | 0  2   3  0 0 |  1  6  3  0 |  3  6  1 | 3 2
x . . . x3o . .   6 |  3  6 |  0   3  2 |  *   * 100  * | 0  0   3  2 0 |  0  3  6  1 |  1  6  3 | 2 3
. . . . x3o3o .   4 |  0  6 |  0   0  4 |  *   *   * 25 | 0  0   0  4 1 |  0  0  6  4 |  0  4  6 | 1 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o . . . .   5 | 10  0 | 10   0  0 |  5   0   0  0 | 5  *   *  * *   4  0  0  0 |  6  0  0 | 4 0
x3o3o . x . . .   8 | 12  4 |  8   6  0 |  2   4   0  0 | * 50   *  * * |  1  3  0  0 |  3  3  0 | 3 1
x3o . . x3o . .   9 |  9  9 |  3   9  3 |  0   3   3  0 | *  * 100  * * |  0  2  2  0 |  1  4  1 | 2 2
x . . . x3o3o .   8 |  4 12 |  0   6  8 |  0   0   4  2 | *  *   * 50 * |  0  0  3  1 |  0  3  3 | 1 3
. . . . x3o3o3o   5 |  0 10 |  0   0 10 |  0   0   0  5 | *  *   *  * 5 |  0  0  0  4 |  0  0  6 | 0 4
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o x . . .  10 | 20  5 | 20  10  0 | 10  10   0  0 | 2  5   0  0 0 | 10  *  *  * |  3  0  0 | 3 0
x3o3o . x3o . .  12 | 18 12 | 12  18  4 |  3  12   6  0 | 0  3   4  0 0 |  * 50  *  * |  1  2  0 | 2 1
x3o . . x3o3o .  12 | 12 18 |  4  18 12 |  0   6  12  3 | 0  0   4  3 0 |  *  * 50  * |  0  2  1 | 1 2
x . . . x3o3o3o  10 |  5 20 |  0  10 20 |  0   0  10 10 | 0  0   0  5 2 |  *  *  * 10 |  0  0  3 | 0 3
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o x3o . .  15 | 30 15 | 30  30  5 | 15  30  10  0 | 3 15  10  0 0 |  3  5  0  0 | 10  *  * | 2 0
x3o3o . x3o3o .  16 | 24 24 | 16  36 16 |  4  24  24  4 | 0  6  16  6 0 |  0  4  4  0 |  * 25  * | 1 1
x3o . . x3o3o3o  15 | 15 30 |  5  30 30 |  0  10  30 15 | 0  0  10 15 3 |  0  0  5  3 |  *  * 10 | 0 2
----------------+----+-------+-----------+---------------+---------------+-------------+----------+----
x3o3o3o x3o3o .  20 | 40 30 | 40  60 20 | 20  60  40  5 | 4 30  40 10 0 |  6 20 10  0 |  4  5  0 | 5 *
x3o3o . x3o3o3o  20 | 30 40 | 20  60 40 |  5  40  60 20 | 0 10  40 30 4 |  0 10 20  6 |  0  5  4 | * 5
or
. . . . . . . .    | 25 |   8 |  12  16 |  8  48 |  2  32  36 |  8  48 | 12 16 |  8
-------------------+----+-----+---------+--------+------------+--------+-------+---
x . . . . . . .  & |  2 | 100 |   3   4 |  3  18 |  1  16  18 |  5  30 |  9 12 |  7
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o . . . . . .  & |  3 |   3 | 100   * |  2   4 |  1   8   6 |  4  16 |  7  8 |  6
x . . . x . . .    |  4 |   4 |   * 100 |  0   6 |  0   6   9 |  2  18 |  6  9 |  6
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o . . . . .  &   4 |   6 |   4   0 | 50   * |  1   4   0 |  4   6 |  6  4 |  5
x3o . . x . . .  &   6 |   9 |   2   3 |  * 200 |  0   2   3 |  1   9 |  4  6 |  5
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o . . . .  &   5 |  10 |  10   0 |  5   0 | 10   *   *   4   0 |  6  0 |  4
x3o3o . x . . .  &   8 |  16 |   8   6 |  2   4 |  * 100   * |  1   3 |  3  3 |  4
x3o . . x3o . .      9 |  18 |   6   9 |  0   6 |  *   * 100 |  0   4 |  2  4 |  4
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o x . . .  &  10 |  25 |  20  10 | 10  10 |  2   5   0 | 20   * |  3  0 |  3
x3o3o . x3o . .  &  12 |  30 |  16  18 |  3  18 |  0   3   4 |  * 100 |  1  2 |  3
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o x3o . .  &  15 |  45 |  35  30 | 15  40 |  3  15  10 |  3   5 | 20  * |  2
x3o3o . x3o3o .     16 |  48 |  32  36 |  8  48 |  0  12  16 |  0   8 |  * 25 |  2
-------------------+----+-----+---------+--------+------------+--------+-------+---
x3o3o3o x3o3o .  &  20 |  70 |  60  60 | 25 100 |  4  40  40 |  6  30 |  4  5 | 10

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