Acronym octpen
Name octahedron - pentachoron duoprism,
vertex figure of tro
Circumradius sqrt(9/10) = 0.948683

Incidence matrix according to Dynkin symbol

x3o4o x3o3o3o

. . . . . . . | 30 |  4  4 |  4  16  6 | 1 16  24  4 |  4 24 16 1 |  6 16  4 | 4 4
--------------+----+-------+-----------+-------------+------------+----------+----
x . . . . . . |  2 | 60  * |  2   4  0 | 1  8   6  0 |  4 12  4 0 |  6  8  1 | 4 2
. . . x . . . |  2 |  * 60 |  0   4  3 | 0  4  12  3 |  1 12 12 1 |  3 12  4 | 3 4
--------------+----+-------+-----------+-------------+------------+----------+----
x3o . . . . . |  3 |  3  0 | 40   *  * | 1  4   0  0 |  4  6  0 0 |  6  4  0 | 4 1
x . . x . . . |  4 |  2  2 |  * 120  * | 0  2   3  0 |  1  6  3 0 |  3  6  1 | 3 2
. . . x3o . . |  3 |  0  3 |  *   * 60 | 0  0   4  2 |  0  4  8 1 |  1  8  4 | 2 4
--------------+----+-------+-----------+-------------+------------+----------+----
x3o4o . . . .   6 | 12  0 |  8   0  0 | 5  *   *  *   4  0  0 0 |  6  0  0 | 4 0
x3o . x . . .   6 |  6  3 |  2   3  0 | * 80   *  * |  1  3  0 0 |  3  3  0 | 3 1
x . . x3o . .   6 |  3  6 |  0   3  2 | *  * 120  * |  0  2  2 0 |  1  4  1 | 2 2
. . . x3o3o .   4 |  0  6 |  0   0  4 | *  *   * 30 |  0  0  4 1 |  0  4  4 | 1 4
--------------+----+-------+-----------+-------------+------------+----------+----
x3o4o x . . .  12 | 24  6 | 16  12  0 | 2  8   0  0 | 10  *  * * |  3  0  0 | 3 0
x3o . x3o . .   9 |  9  9 |  3   9  3 | 0  3   3  0 |  * 80  * * |  1  2  0 | 2 1
x . . x3o3o .   8 |  4 12 |  0   6  8 | 0  0   4  2 |  *  * 60 * |  0  2  1 | 1 2
. . . x3o3o3o   5 |  0 10 |  0   0 10 | 0  0   0  5 |  *  *  * 6 |  0  0  4 | 0 4
--------------+----+-------+-----------+-------------+------------+----------+----
x3o4o x3o . .  18 | 36 18 | 24  36  6 | 3 24  12  0 |  3  8  0 0 | 10  *  * | 2 0
x3o . x3o3o .  12 | 12 18 |  4  18 12 | 0  6  12  3 |  0  4  3 0 |  * 40  * | 1 1
x . . x3o3o3o  10 |  5 20 |  0  10 20 | 0  0  10 10 |  0  0  5 2 |  *  * 12 | 0 2
--------------+----+-------+-----------+-------------+------------+----------+----
x3o4o x3o3o .  24 | 48 36 | 32  72 24 | 4 48  48  6 |  6 32 12 0 |  4  8  0 | 5 *
x3o . x3o3o3o  15 | 15 30 |  5  30 30 | 0 10  30 15 |  0 10 15 3 |  0  5  3 | * 8

o3x3o x3o3o3o

. . . . . . . | 30 |  4  4 |  2  2  16  6 | 1  8  8  24  4 |  4 12 12 16 1 |  6  8  8  4 | 4 2 2
--------------+----+-------+--------------+----------------+---------------+-------------+------
. x . . . . . |  2 | 60  * |  1  1   4  0 | 1  4  4   6  0 |  4  6  6  4 0 |  6  4  4  1 | 4 1 1
. . . x . . . |  2 |  * 60 |  0  0   4  3 | 0  2  2  12  3 |  1  6  6 12 1 |  3  6  6  4 | 3 2 2
--------------+----+-------+--------------+----------------+---------------+-------------+------
o3x . . . . . |  3 |  3  0 | 20  *   *  * | 1  4  0   0  0 |  4  6  0  0 0 |  6  4  0  0 | 4 1 0
. x3o . . . . |  3 |  3  0 |  * 20   *  * | 1  0  4   0  0 |  4  0  6  0 0 |  6  0  4  0 | 4 0 1
. x . x . . . |  4 |  2  2 |  *  * 120  * | 0  1  1   3  0 |  1  3  3  3 0 |  3  3  3  1 | 3 1 1
. . . x3o . . |  3 |  0  3 |  *  *   * 60 | 0  0  0   4  2 |  0  2  2  8 1 |  1  4  4  4 | 2 2 2
--------------+----+-------+--------------+----------------+---------------+-------------+------
o3x3o . . . .   6 | 12  0 |  4  4   0  0 | 5  *  *   *  *   4  0  0  0 0 |  6  0  0  0 | 4 0 0
o3x . x . . .   6 |  6  3 |  2  0   3  0 | * 40  *   *  * |  1  3  0  0 0 |  3  3  0  0 | 3 1 0
. x3o x . . .   6 |  6  3 |  0  2   3  0 | *  * 40   *  * |  1  0  3  0 0 |  3  0  3  0 | 3 0 1
. x . x3o . .   6 |  3  6 |  0  0   3  2 | *  *  * 120  * |  0  1  1  2 0 |  1  2  2  1 | 2 1 1
. . . x3o3o .   4 |  0  6 |  0  0   0  4 | *  *  *   * 30 |  0  0  0  4 1 |  0  2  2  4 | 1 2 2
--------------+----+-------+--------------+----------------+---------------+-------------+------
o3x3o x . . .  12 | 24  6 |  8  8  12  0 | 2  4  4   0  0 | 10  *  *  * * |  3  0  0  0 | 3 0 0
o3x . x3o . .   9 |  9  9 |  3  0   9  3 | 0  3  0   3  0 |  * 40  *  * * |  1  2  0  0 | 2 1 0
. x3o x3o . .   9 |  9  9 |  0  3   9  3 | 0  0  3   3  0 |  *  * 40  * * |  1  0  2  0 | 2 0 1
. x . x3o3o .   8 |  4 12 |  0  0   6  8 | 0  0  0   4  2 |  *  *  * 60 * |  0  1  1  1 | 1 1 1
. . . x3o3o3o   5 |  0 10 |  0  0   0 10 | 0  0  0   0  5 |  *  *  *  * 6 |  0  0  0  4 | 0 2 2
--------------+----+-------+--------------+----------------+---------------+-------------+------
o3x3o x3o . .  18 | 36 18 | 12 12  36  6 | 3 12 12  12  0 |  3  4  4  0 0 | 10  *  *  * | 2 0 0
o3x . x3o3o .  12 | 12 18 |  4  0  18 12 | 0  6  0  12  3 |  0  4  0  3 0 |  * 20  *  * | 1 1 0
. x3o x3o3o .  12 | 12 18 |  0  4  18 12 | 0  0  6  12  3 |  0  0  4  3 0 |  *  * 20  * | 1 0 1
. x . x3o3o3o  10 |  5 20 |  0  0  10 20 | 0  0  0  10 10 |  0  0  0  5 2 |  *  *  * 12 | 0 1 1
--------------+----+-------+--------------+----------------+---------------+-------------+------
o3x3o x3o3o .  24 | 48 36 | 16 16  72 24 | 4 24 24  48  6 |  6 16 16 12 0 |  4  4  4  0 | 5 * *
o3x . x3o3o3o  15 | 15 30 |  5  0  30 30 | 0 10  0  30 15 |  0 10  0 15 3 |  0  5  0  3 | * 4 *
. x3o x3o3o3o  15 | 15 30 |  0  5  30 30 | 0  0 10  30 15 |  0  0 10 15 3 |  0  0  5  3 | * * 4

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