Acronym copen
Name cuboctahedron - pentachoron duoprism
Circumradius sqrt(7/5) = 1.183216

Incidence matrix according to Dynkin symbol

o3x4o x3o3o3o

. . . . . . . | 60 |   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 | 120   * |  1  1   4   0 | 1  4  4   6  0 |  4  6  6   4  0 |  6  4  4  1 | 4 1 1
. . . x . . . |  2 |   * 120 |  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 | 40  *   *   * | 1  4  0   0  0 |  4  6  0   0  0 |  6  4  0  0 | 4 1 0
. x4o . . . . |  4 |   4   0 |  * 30   *   * | 1  0  4   0  0 |  4  0  6   0  0 |  6  0  4  0 | 4 0 1
. x . x . . . |  4 |   2   2 |  *  * 240   * | 0  1  1   3  0 |  1  3  3   3  0 |  3  3  3  1 | 3 1 1
. . . x3o . . |  3 |   0   3 |  *  *   * 120 | 0  0  0   4  2 |  0  2  2   8  1 |  1  4  4  4 | 2 2 2
--------------+----+---------+---------------+----------------+-----------------+-------------+------
o3x4o . . . .  12 |  24   0 |  8  6   0   0 | 5  *  *   *  *   4  0  0   0  0 |  6  0  0  0 | 4 0 0
o3x . x . . .   6 |   6   3 |  2  0   3   0 | * 80  *   *  * |  1  3  0   0  0 |  3  3  0  0 | 3 1 0
. x4o x . . .   8 |   8   4 |  0  2   4   0 | *  * 60   *  * |  1  0  3   0  0 |  3  0  3  0 | 3 0 1
. x . x3o . .   6 |   3   6 |  0  0   3   2 | *  *  * 240  * |  0  1  1   2  0 |  1  2  2  1 | 2 1 1
. . . x3o3o .   4 |   0   6 |  0  0   0   4 | *  *  *   * 60 |  0  0  0   4  1 |  0  2  2  4 | 1 2 2
--------------+----+---------+---------------+----------------+-----------------+-------------+------
o3x4o x . . .  24 |  48  12 | 16 12  24   0 | 2  8  6   0  0 | 10  *  *   *  * |  3  0  0  0 | 3 0 0
o3x . x3o . .   9 |   9   9 |  3  0   9   3 | 0  3  0   3  0 |  * 80  *   *  * |  1  2  0  0 | 2 1 0
. x4o x3o . .  12 |  12  12 |  0  3  12   4 | 0  0  3   4  0 |  *  * 60   *  * |  1  0  2  0 | 2 0 1
. x . x3o3o .   8 |   4  12 |  0  0   6   8 | 0  0  0   4  2 |  *  *  * 120  * |  0  1  1  1 | 1 1 1
. . . x3o3o3o   5 |   0  10 |  0  0   0  10 | 0  0  0   0  5 |  *  *  *   * 12 |  0  0  0  4 | 0 2 2
--------------+----+---------+---------------+----------------+-----------------+-------------+------
o3x4o x3o . .  36 |  72  36 | 24 18  72  12 | 3 24 18  24  0 |  3  8  6   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 |  * 40  *  * | 1 1 0
. x4o x3o3o .  16 |  16  24 |  0  4  24  16 | 0  0  6  16  4 |  0  0  4   4  0 |  *  * 30  * | 1 0 1
. x . x3o3o3o  10 |   5  20 |  0  0  10  20 | 0  0  0  10 10 |  0  0  0   5  2 |  *  *  * 24 | 0 1 1
--------------+----+---------+---------------+----------------+-----------------+-------------+------
o3x4o x3o3o .  48 |  96  72 | 32 24 144  48 | 4 48 36  96 12 |  6 32 24  24  0 |  4  8  6  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 | * 8 *
. x4o x3o3o3o  20 |  20  40 |  0  5  40  40 | 0  0 10  40 20 |  0  0 10  20  4 |  0  0  5  4 | * * 6

x3o3x x3o3o3o

. . . . . . . | 60 |  2  2   4 |  1  2   8  1   8   6 | 1  4  8  12  4  12  4 |  4  6 12  8  6  8  1 |  6  4  8  2  4  2 | 4 1 2 1
--------------+----+-----------+----------------------+-----------------------+----------------------+-------------------+--------
x . . . . . . |  2 | 60  *   * |  1  1   4  0   0   0 | 1  4  4   6  0   0  0 |  4  6  6  4  0  0  0 |  6  4  4  1  0  0 | 4 1 1 0
. . x . . . . |  2 |  * 60   * |  0  1   0  1   4   0 | 1  0  4   0  4   6  0 |  4  0  6  0  6  4  0 |  6  0  4  0  4  1 | 4 0 1 1
. . . x . . . |  2 |  *  * 120 |  0  0   2  0   2   3 | 0  1  2   6  1   6  3 |  1  3  6  6  3  6  1 |  3  3  6  2  3  2 | 3 1 2 1
--------------+----+-----------+----------------------+-----------------------+----------------------+-------------------+--------
x3o . . . . . |  3 |  3  0   0 | 20  *   *  *   *   * | 1  4  0   0  0   0  0 |  4  6  0  0  0  0  0 |  6  4  0  0  0  0 | 4 1 0 0
x . x . . . . |  4 |  2  2   0 |  * 30   *  *   *   * | 1  0  4   0  0   0  0 |  4  0  6  0  0  0  0 |  6  0  4  0  0  0 | 4 0 1 0
x . . x . . . |  4 |  2  0   2 |  *  * 120  *   *   * | 0  1  1   3  0   0  0 |  1  3  3  3  0  0  0 |  3  3  3  1  0  0 | 3 1 1 0
. o3x . . . . |  3 |  0  3   0 |  *  *   * 20   *   * | 1  0  0   0  4   0  0 |  4  0  0  0  6  0  0 |  6  0  0  0  4  0 | 4 0 0 1
. . x x . . . |  4 |  0  2   2 |  *  *   *  * 120   * | 0  0  1   0  1   3  0 |  1  0  3  0  3  3  0 |  3  0  3  0  3  1 | 3 0 1 1
. . . x3o . . |  3 |  0  0   3 |  *  *   *  *   * 120 | 0  0  0   2  0   2  2 |  0  1  2  4  1  4  1 |  1  2  4  2  2  2 | 2 1 2 1
--------------+----+-----------+----------------------+-----------------------+----------------------+-------------------+--------
x3o3x . . . .  12 | 12 12   0 |  4  6   0  4   0   0 | 5  *  *   *  *   *  *   4  0  0  0  0  0  0 |  6  0  0  0  0  0 | 4 0 0 0
x3o . x . . .   6 |  6  0   3 |  2  0   3  0   0   0 | * 40  *   *  *   *  * |  1  3  0  0  0  0  0 |  3  3  0  0  0  0 | 3 1 0 0
x . x x . . .   8 |  4  4   4 |  0  2   2  0   2   0 | *  * 60   *  *   *  * |  1  0  3  0  0  0  0 |  3  0  3  0  0  0 | 3 0 1 0
x . . x3o . .   6 |  3  0   6 |  0  0   3  0   0   2 | *  *  * 120  *   *  * |  0  1  1  2  0  0  0 |  1  2  2  1  0  0 | 2 1 1 0
. o3x x . . .   6 |  0  6   3 |  0  0   0  2   3   0 | *  *  *   * 40   *  * |  1  0  0  0  3  0  0 |  3  0  0  0  3  0 | 3 0 0 1
. . x x3o . .   6 |  0  3   6 |  0  0   0  0   3   2 | *  *  *   *  * 120  * |  0  0  1  0  1  2  0 |  1  0  2  0  2  1 | 2 0 1 1
. . . x3o3o .   4 |  0  0   6 |  0  0   0  0   0   4 | *  *  *   *  *   * 60 |  0  0  0  2  0  2  1 |  0  1  2  2  1  2 | 1 1 2 1
--------------+----+-----------+----------------------+-----------------------+----------------------+-------------------+--------
x3o3x x . . .  24 | 24 24  12 |  8 12  12  8  12   0 | 2  4  6   0  4   0  0 | 10  *  *  *  *  *  * |  3  0  0  0  0  0 | 3 0 0 0
x3o . x3o . .   9 |  9  0   9 |  3  0   9  0   0   3 | 0  3  0   3  0   0  0 |  * 40  *  *  *  *  * |  1  2  0  0  0  0 | 2 1 0 0
x . x x3o . .  12 |  6  6  12 |  0  3   6  0   6   4 | 0  0  3   2  0   2  0 |  *  * 60  *  *  *  * |  1  0  2  0  0  0 | 2 0 1 0
x . . x3o3o .   8 |  4  0  12 |  0  0   6  0   0   8 | 0  0  0   4  0   0  2 |  *  *  * 60  *  *  * |  0  1  1  1  0  0 | 1 1 1 0
. o3x x3o . .   9 |  0  9   9 |  0  0   0  3   9   3 | 0  0  0   0  3   3  0 |  *  *  *  * 40  *  * |  1  0  0  0  2  0 | 2 0 0 1
. . x x3o3o .   8 |  0  4  12 |  0  0   0  0   6   8 | 0  0  0   0  0   4  2 |  *  *  *  *  * 60  * |  0  0  1  0  1  1 | 1 0 1 1
. . . x3o3o3o   5 |  0  0  10 |  0  0   0  0   0  10 | 0  0  0   0  0   0  5 |  *  *  *  *  *  * 12 |  0  0  0  2  0  2 | 0 1 2 1
--------------+----+-----------+----------------------+-----------------------+----------------------+-------------------+--------
x3o3x x3o . .  36 | 36 36  36 | 12 18  36 12  36  12 | 3 12 18  12 12  12  0 |  3  4  6  0  4  0  0 | 10  *  *  *  *  * | 2 0 0 0
x3o . x3o3o .  12 | 12  0  18 |  4  0  18  0   0  12 | 0  6  0  12  0   0  3 |  0  4  0  3  0  0  0 |  * 20  *  *  *  * | 1 1 0 0
x . x x3o3o .  16 |  8  8  24 |  0  4  12  0  12  16 | 0  0  6   8  0   8  4 |  0  0  4  2  0  2  0 |  *  * 30  *  *  * | 1 0 1 0
x . . x3o3o3o  10 |  5  0  20 |  0  0  10  0   0  20 | 0  0  0  10  0   0 10 |  0  0  0  5  0  0  2 |  *  *  * 12  *  * | 0 1 1 0
. o3x x3o3o .  12 |  0 12  18 |  0  0   0  4  18  12 | 0  0  0   0  6  12  3 |  0  0  0  0  4  3  0 |  *  *  *  * 20  * | 1 0 0 1
. . x x3o3o3o  10 |  0  5  20 |  0  0   0  0  10  20 | 0  0  0   0  0  10 10 |  0  0  0  0  0  5  2 |  *  *  *  *  * 12 | 0 0 1 1
--------------+----+-----------+----------------------+-----------------------+----------------------+-------------------+--------
x3o3x x3o3o .  48 | 48 48  72 | 16 24  72 16  72  48 | 4 24 36  48 24  48 12 |  6 16 24 12 16 12  0 |  4  4  6  0  4  0 | 5 * * *
x3o . x3o3o3o  15 | 15  0  30 |  5  0  30  0   0  30 | 0 10  0  30  0   0 15 |  0 10  0 15  0  0  3 |  0  5  0  3  0  0 | * 4 * *
x . x x3o3o3o  20 | 10 10  40 |  0  5  20  0  20  40 | 0  0 10  20  0  20 20 |  0  0 10 10  0 10  4 |  0  0  5  2  0  2 | * * 6 *
. o3x x3o3o3o  15 |  0 15  30 |  0  0   0  5  30  30 | 0  0  0   0 10  30 15 |  0  0  0  0 10 15  3 |  0  0  0  0  5  3 | * * * 4

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