Acronym octid
Name octahedron-icosidodecahedron duoprism
Circumradius sqrt[(4+sqrt(5))/2] = 1.765796

Incidence matrix according to Dynkin symbol

x3o4o o3x5o

. . . . . . | 180 |   4   4 |   4  16   2  2 |  1  16   8   8 1 |  4   8  8  4 |  2  2 4
------------+-----+---------+----------------+------------------+--------------+--------
x . . . . . |   2 | 360   * |   2   4   0  0 |  1   8   2   2 0 |  4   4  4  1 |  2  2 2
. . . . x . |   2 |   * 360 |   0   4   1  1 |  0   4   4   4 1 |  1   4  4  4 |  1  1 4
------------+-----+---------+----------------+------------------+--------------+--------
x3o . . . . |   3 |   3   0 | 240   *   *  * |  1   4   0   0 0 |  4   2  2  0 |  2  2 1
x . . . x . |   4 |   2   2 |   * 720   *  * |  0   2   1   1 0 |  1   2  2  1 |  1  1 2
. . . o3x . |   3 |   0   3 |   *   * 120  * |  0   0   4   0 1 |  0   4  0  4 |  1  0 4
. . . . x5o |   5 |   0   5 |   *   *   * 72 |  0   0   0   4 1 |  0   0  4  4 |  0  1 4
------------+-----+---------+----------------+------------------+--------------+--------
x3o4o . . .    6 |  12   0 |   8   0   0  0 | 30   *   *   * * |  4   0  0  0 |  2  2 0
x3o . . x .    6 |   6   3 |   2   3   0  0 |  * 480   *   * * |  1   1  1  0 |  1  1 1
x . . o3x .    6 |   3   6 |   0   3   2  0 |  *   * 240   * * |  0   2  0  1 |  1  0 2
x . . . x5o   10 |   5  10 |   0   5   0  2 |  *   *   * 144 * |  0   0  2  1 |  0  1 2
. . . o3x5o   30 |   0  60 |   0   0  20 12 |  *   *   *   * 6 |  0   0  0  4 |  0  0 4
------------+-----+---------+----------------+------------------+--------------+--------
x3o4o . x .   12 |  24   6 |  16  12   0  0 |  2   8   0   0 0 | 60   *  *  * |  1  1 0
x3o . o3x .    9 |   9   9 |   3   9   3  0 |  0   3   3   0 0 |  * 160  *  * |  1  0 1
x3o . . x5o   15 |  15  15 |   5  15   0  3 |  0   5   0   3 0 |  *   * 96  * |  0  1 1
x . . o3x5o   60 |  30 120 |   0  60  40 24 |  0   0  20  12 2 |  *   *  * 12 |  0  0 2
------------+-----+---------+----------------+------------------+--------------+--------
x3o4o o3x .   18 |  36  18 |  24  36   6  0 |  3  24  12   0 0 |  3   8  0  0 | 20  * *
x3o4o . x5o   30 |  60  30 |  40  60   0  6 |  5  40   0  12 0 |  5   0  8  0 |  * 12 *
x3o . o3x5o   90 |  90 180 |  30 180  60 36 |  0  60  60  36 3 |  0  20 12  3 |  *  * 8

o3x3o o3x5o

. . . . . . | 180 |   4   4 |   2   2  16   2  2 |  1   8   8   8   8 1 |  4  4  4  4  4  4 |  2  2 2 2
------------+-----+---------+--------------------+----------------------+-------------------+----------
. x . . . . |   2 | 360   * |   1   1   4   0  0 |  1   4   4   2   2 0 |  4  2  2  2  2  1 |  2  2 1 1
. . . . x . |   2 |   * 360 |   0   0   4   1  1 |  0   2   2   4   4 1 |  1  2  2  2  2  4 |  1  1 2 2
------------+-----+---------+--------------------+----------------------+-------------------+----------
o3x . . . . |   3 |   3   0 | 120   *   *   *  * |  1   4   0   0   0 0 |  4  2  2  0  0  0 |  2  2 1 0
. x3o . . . |   3 |   3   0 |   * 120   *   *  * |  1   0   4   0   0 0 |  4  0  0  2  2  0 |  2  2 0 1
. x . . x . |   4 |   2   2 |   *   * 720   *  * |  0   1   1   1   1 0 |  1  1  1  1  1  1 |  1  1 1 1
. . . o3x . |   3 |   0   3 |   *   *   * 120  * |  0   0   0   4   0 1 |  0  2  0  2  0  4 |  1  0 2 2
. . . . x5o |   5 |   0   5 |   *   *   *   * 72 |  0   0   0   0   4 1 |  0  0  2  0  2  4 |  0  1 2 2
------------+-----+---------+--------------------+----------------------+-------------------+----------
o3x3o . . .    6 |  12   0 |   4   4   0   0  0 | 30   *   *   *   * * |  4  0  0  0  0  0 |  2  2 0 0
o3x . . x .    6 |   6   3 |   2   0   3   0  0 |  * 240   *   *   * * |  1  1  1  0  0  0 |  1  1 1 0
. x3o . x .    6 |   6   3 |   0   2   3   0  0 |  *   * 240   *   * * |  1  0  0  1  1  0 |  1  1 0 1
. x . o3x .    6 |   3   6 |   0   0   3   2  0 |  *   *   * 240   * * |  0  1  0  1  0  1 |  1  0 1 1
. x . . x5o   10 |   5  10 |   0   0   5   0  2 |  *   *   *   * 144 * |  0  0  1  0  1  1 |  0  1 1 1
. . . o3x5o   30 |   0  60 |   0   0   0  20 12 |  *   *   *   *   * 6 |  0  0  0  0  0  4 |  0  0 2 2
------------+-----+---------+--------------------+----------------------+-------------------+----------
o3x3o . x .   12 |  24   6 |   8   8  12   0  0 |  2   4   4   0   0 0 | 60  *  *  *  *  * |  1  1 0 0
o3x . o3x .    9 |   9   9 |   3   0   9   3  0 |  0   3   0   3   0 0 |  * 80  *  *  *  * |  1  0 1 0
o3x . . x5o   15 |  15  15 |   5   0  15   0  3 |  0   5   0   0   3 0 |  *  * 48  *  *  * |  0  1 1 0
. x3o o3x .    9 |   9   9 |   0   3   9   3  0 |  0   0   3   3   0 0 |  *  *  * 80  *  * |  1  0 0 1
. x3o . x5o   15 |  15  15 |   0   5  15   0  3 |  0   0   5   0   3 0 |  *  *  *  * 48  * |  0  1 0 1
. x . o3x5o   60 |  30 120 |   0   0  60  40 24 |  0   0   0  20  12 2 |  *  *  *  *  * 12 |  0  0 1 1
------------+-----+---------+--------------------+----------------------+-------------------+----------
o3x3o o3x .   18 |  36  18 |  12  12  36   6  0 |  3  12  12  12   0 0 |  3  4  0  4  0  0 | 20  * * *
o3x3o . x5o   30 |  60  30 |  20  20  60   0  6 |  5  20  20   0  12 0 |  5  0  4  0  4  0 |  * 12 * *
o3x . o3x5o   90 |  90 180 |  30   0 180  60 36 |  0  60   0  60  36 3 |  0 20 12  0  0  3 |  *  * 4 *
. x3o o3x5o   90 |  90 180 |   0  30 180  60 36 |  0   0  60  60  36 3 |  0  0  0 20 12  3 |  *  * * 4

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