Acronym n,oct-dippip
Name n-gon - octahedron duoprismatic prism
Especially trope (n=3)   octcube (n=4)  

Incidence matrix according to Dynkin symbol

x xno x3o4o   (n>2)

. . . . . . | 12n |  1   2   4 |  2   4  1   8   4 | 1   8  4  4   8  1 |  4  8 1  4  2 | 4 2 1
------------+-----+------------+-------------------+--------------------+---------------+------
x . . . . . |   2 | 6n   *   * |  2   4  0   0   0 | 1   8  4  0   0  0 |  4  8 1  0  0 | 4 2 0
. x . . . . |   2 |  * 12n   * |  1   0  1   4   0 | 1   4  0  4   4  0 |  4  4 0  4  1 | 4 1 1
. . . x . . |   2 |  *   * 24n |  0   1  0   2   2 | 0   2  2  1   4  1 |  1  4 1  2  2 | 2 2 1
------------+-----+------------+-------------------+--------------------+---------------+------
x x . . . . |   4 |  2   2   0 | 6n   *  *   *   * | 1   4  0  0   0  0 |  4  4 0  0  0 | 4 1 0
x . . x . . |   4 |  2   0   2 |  * 12n  *   *   * | 0   2  2  0   0  0 |  1  4 1  0  0 | 2 2 0
. xno . . . |   n |  0   n   0 |  *   * 12   *   * | 1   0  0  4   0  0 |  4  0 0  4  0 | 4 0 1
. x . x . . |   4 |  0   2   2 |  *   *  * 24n   * | 0   1  0  1   2  0 |  1  2 0  2  1 | 2 1 1
. . . x3o . |   3 |  0   0   3 |  *   *  *   * 16n | 0   0  1  0   2  1 |  0  2 1  1  2 | 1 2 1
------------+-----+------------+-------------------+--------------------+---------------+------
x xno . . .   2n |  n  2n   0 |  n   0  2   0   0 | 6   *  *  *   *  * |  4  0 0  0  0 | 4 0 0
x x . x . .    8 |  4   4   4 |  2   2  0   2   0 | * 12n  *  *   *  * |  1  2 0  0  0 | 2 1 0
x . . x3o .    6 |  3   0   6 |  0   3  0   0   2 | *   * 8n  *   *  * |  0  2 1  0  0 | 1 2 0
. xno x . .   2n |  0  2n   n |  0   0  2   n   0 | *   *  * 24   *  * |  1  0 0  2  0 | 2 0 1
. x . x3o .    6 |  0   3   6 |  0   0  0   3   2 | *   *  *  * 16n  * |  0  1 0  1  1 | 1 1 1
. . . x3o4o    6 |  0   0  12 |  0   0  0   0   8 | *   *  *  *   * 2n |  0  0 1  0  2 | 0 2 1
------------+-----+------------+-------------------+--------------------+---------------+------
x xno x . .   4n | 2n  4n  2n | 2n   n  4  2n   0 | 2   n  0  2   0  0 | 12  * *  *  * | 2 0 0
x x . x3o .   12 |  6   6  12 |  3   6  0   6   4 | 0   3  2  0   2  0 |  * 8n *  *  * | 1 1 0
x . . x3o4o   12 |  6   0  24 |  0  12  0   0  16 | 0   0  8  0   0  2 |  *  * n  *  * | 0 2 0
. xno x3o .   3n |  0  3n  3n |  0   0  3  3n   n | 0   0  0  3   n  0 |  *  * * 16  * | 1 0 1
. x . x3o4o   12 |  0   6  24 |  0   0  0  12  16 | 0   0  0  0   8  2 |  *  * *  * 2n | 0 1 1
------------+-----+------------+-------------------+--------------------+---------------+------
x xno x3o .   6n | 3n  6n  6n | 3n  3n  6  6n  2n | 3  3n  n  6  2n  0 |  3  n 0  2  0 | 8 * *
x x . x3o4o   24 | 12  12  48 |  6  24  0  24  32 | 0  12 16  0  16  4 |  0  8 2  0  2 | * n *
. xno x3o4o   6n |  0  6n 12n |  0   0  6 12n  8n | 0   0  0 12  8n  n |  0  0 0  8  n | * * 2

x xno o3x3o   (n>2)

. . . . . . | 12n |  1   2   4 |  2   4  1   8  2  2 | 1   8  2  2  4  4  4  1 |  4  4  4 1 2 2  2 | 2 2 2 1
------------+-----+------------+---------------------+-------------------------+-------------------+--------
x . . . . . |   2 | 6n   *   * |  2   4  0   0  0  0 | 1   8  2  2  0  0  0  0 |  4  4  4 1 0 0  0 | 2 2 2 0
. x . . . . |   2 |  * 12n   * |  1   0  1   4  0  0 | 1   4  0  0  4  2  2  0 |  4  2  2 0 2 2  1 | 2 2 1 1
. . . . x . |   2 |  *   * 24n |  0   1  0   2  1  1 | 0   2  1  1  1  2  2  1 |  1  2  2 1 1 1  2 | 1 1 2 1
------------+-----+------------+---------------------+-------------------------+-------------------+--------
x x . . . . |   4 |  2   2   0 | 6n   *  *   *  *  * | 1   4  0  0  0  0  0  0 |  4  2  2 0 0 0  0 | 2 2 1 0
x . . . x . |   4 |  2   0   2 |  * 12n  *   *  *  * | 0   2  1  1  0  0  0  0 |  1  2  2 1 0 0  0 | 1 1 2 0
. xno . . . |   n |  0   n   0 |  *   * 12   *  *  * | 1   0  0  0  4  0  0  0 |  4  0  0 0 2 2  0 | 2 2 0 1
. x . . x . |   4 |  0   2   2 |  *   *  * 24n  *  * | 0   1  0  0  1  1  1  0 |  1  1  1 0 1 1  1 | 1 1 1 1
. . . o3x . |   3 |  0   0   3 |  *   *  *   * 8n  * | 0   0  1  0  0  2  0  1 |  0  2  0 1 1 0  2 | 1 0 2 1
. . . . x3o |   3 |  0   0   3 |  *   *  *   *  * 8n | 0   0  0  1  0  0  2  1 |  0  0  2 1 0 1  2 | 0 1 2 1
------------+-----+------------+---------------------+-------------------------+-------------------+--------
x xno . . .   2n |  n  2n   0 |  n   0  2   0  0  0 | 6   *  *  *  *  *  *  * |  4  0  0 0 0 0  0 | 2 2 0 0
x x . . x .    8 |  4   4   4 |  2   2  0   2  0  0 | * 12n  *  *  *  *  *  * |  1  1  1 0 0 0  0 | 1 1 1 0
x . . o3x .    6 |  3   0   6 |  0   3  0   0  2  0 | *   * 4n  *  *  *  *  * |  0  2  0 1 0 0  0 | 1 0 2 0
x . . . x3o    6 |  3   0   6 |  0   3  0   0  0  2 | *   *  * 4n  *  *  *  * |  0  0  2 1 0 0  0 | 0 1 2 0
. xno . x .   2n |  0  2n   n |  0   0  2   n  0  0 | *   *  *  * 24  *  *  * |  1  0  0 0 1 1  0 | 1 1 0 1
. x . o3x .    6 |  0   3   6 |  0   0  0   3  2  0 | *   *  *  *  * 8n  *  * |  0  1  0 0 1 0  1 | 1 0 1 1
. x . . x3o    6 |  0   3   6 |  0   0  0   3  0  2 | *   *  *  *  *  * 8n  * |  0  0  1 0 0 1  1 | 0 1 1 1
. . . o3x3o    6 |  0   0  12 |  0   0  0   0  4  4 | *   *  *  *  *  *  * 2n |  0  0  0 1 0 0  2 | 0 0 2 1
------------+-----+------------+---------------------+-------------------------+-------------------+--------
x xno . x .   4n | 2n  4n  2n | 2n   n  4  2n  0  0 | 2   n  0  0  2  0  0  0 | 12  *  * * * *  * | 1 1 0 0
x x . o3x .   12 |  6   6  12 |  3   6  0   6  4  0 | 0   3  2  0  0  2  0  0 |  * 4n  * * * *  * | 1 0 1 0
x x . . x3o   12 |  6   6  12 |  3   6  0   6  0  4 | 0   3  0  2  0  0  2  0 |  *  * 4n * * *  * | 0 1 1 0
x . . o3x3o   12 |  6   0  24 |  0  12  0   0  8  8 | 0   0  4  4  0  0  0  2 |  *  *  * n * *  * | 0 0 2 0
. xno o3x .   3n |  0  3n  3n |  0   0  3  3n  n  0 | 0   0  0  0  3  n  0  0 |  *  *  * * 8 *  * | 1 0 0 1
. xno . x3o   3n |  0  3n  3n |  0   0  3  3n  0  n | 0   0  0  0  3  0  n  0 |  *  *  * * * 8  * | 0 1 0 1
. x . o3x3o   12 |  0   6  24 |  0   0  0  12  8  8 | 0   0  0  0  0  4  4  2 |  *  *  * * * * 2n | 0 0 1 1
------------+-----+------------+---------------------+-------------------------+-------------------+--------
x xno o3x .   6n | 3n  6n  6n | 3n  3n  6  6n 2n  0 | 3  3n  n  0  6 2n  0  0 |  3  n  0 0 2 0  0 | 4 * * *
x xno . x3o   6n | 3n  6n  6n | 3n  3n  6  6n  0 2n | 3  3n  0  n  6  0 2n  0 |  3  0  n 0 2 0  0 | * 4 * *
x x . o3x3o   24 | 12  12  48 |  6  24  0  24 16 16 | 0  12  8  8  0  8  8  4 |  0  4  4 2 0 0  2 | * * n *
. xno o3x3o   6n |  0  6n 12n |  0   0  6 12n 4n 4n | 0   0  0  0 12 4n 4n  n |  0  0  0 0 4 4  n | * * * 2

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