Acronym octhex
Name octahedron - hexadecachoron duoprism,
vertex figure of troch
Circumradius 1

Incidence matrix according to Dynkin symbol

x3o4o x3o3o4o

o3o4o o3o3o4o | 48 |  4   6 |  4  24  12 | 1  24  48  8 |  6  48  32 1 | 12  32  4 |  8 4
--------------+----+--------+------------+--------------+--------------+-----------+-----
x . . . . . . |  2 | 96   * |  2   6   0 | 1  12  12  0 |  6  24   8 0 | 12  16  1 |  8 2
. . . x . . . |  2 |  * 144 |  0   4   4 | 0   4  16  4 |  1  16  16 1 |  4  16  4 |  4 4
--------------+----+--------+------------+--------------+--------------+-----------+-----
x3o . . . . . |  3 |  3   0 | 64   *   * | 1   6   0  0 |  6  12   0 0 | 12   8  0 |  8 1
x . . x . . . |  4 |  2   2 |  * 288   * | 0   2   4  0 |  1   8   4 0 |  4   8  1 |  4 2
. . . x3o . . |  3 |  0   3 |  *   * 192 | 0   0   4  2 |  0   4   8 1 |  1   8  4 |  2 4
--------------+----+--------+------------+--------------+--------------+-----------+-----
x3o4o . . . .   6 | 12   0 |  8   0   0 | 8   *   *  *   6   0   0 0 | 12   0  0 |  8 0
x3o . x . . .   6 |  6   3 |  2   3   0 | * 192   *  * |  1   4   0 0 |  4   4  0 |  4 1
x . . x3o . .   6 |  3   6 |  0   3   2 | *   * 384  * |  0   2   2 0 |  1   4  1 |  2 2
. . . x3o3o .   4 |  0   6 |  0   0   4 | *   *   * 96 |  0   0   4 1 |  0   4  4 |  1 4
--------------+----+--------+------------+--------------+--------------+-----------+-----
x3o4o x . . .  12 | 24   6 | 16  12   0 | 2   8   0  0 | 24   *   * * |  4   0  0 |  4 0
x3o . x3o . .   9 |  9   9 |  3   9   3 | 0   3   3  0 |  * 256   * * |  1   2  0 |  2 1
x . . x3o3o .   8 |  4  12 |  0   6   8 | 0   0   4  2 |  *   * 192 * |  0   2  1 |  1 2
. . . x3o3o4o   8 |  0  24 |  0   0  32 | 0   0   0 16 |  *   *   * 6 |  0   0  4 |  0 4
--------------+----+--------+------------+--------------+--------------+-----------+-----
x3o4o x3o . .  18 | 36  18 | 24  36   6 | 3  24  12  0 |  3   8   0 0 | 32   *  * |  2 0
x3o . x3o3o .  12 | 12  18 |  4  18  12 | 0   6  12  3 |  0   4   3 0 |  * 128  * |  1 1
x . . x3o3o4o  16 |  8  48 |  0  24  64 | 0   0  32 32 |  0   0  16 2 |  *   * 12 |  0 2
--------------+----+--------+------------+--------------+--------------+-----------+-----
x3o4o x3o3o .  24 | 48  48 | 32  72  24 | 4  48  48  6 |  6  32  12 0 |  4   8  0 | 16 *
x3o . x3o3o4o  24 | 24  72 |  8  72  96 | 0  24  96 48 |  0  32  48 3 |  0  16  3 |  * 8

o3x3o x3o3o4o

o3o3o o3o3o4o | 48 |  4   6 |  2  2  24  12 | 1 12 12  48  8 |  6  24  24  32 1 | 12 16 16  4 |  8 2 2
--------------+----+--------+---------------+----------------+------------------+-------------+-------
. x . . . . . |  2 | 96   * |  1  1   6   0 | 1  6  6  12  0 |  6  12  12   8 0 | 12  8  8  1 |  8 1 1
. . . x . . . |  2 |  * 144 |  0  0   4   4 | 0  2  2  16  4 |  1   8   8  16 1 |  4  8  8  4 |  4 2 2
--------------+----+--------+---------------+----------------+------------------+-------------+-------
o3x . . . . . |  3 |  3   0 | 32  *   *   * | 1  6  0   0  0 |  6  12   0   0 0 | 12  8  0  0 |  8 1 0
. x3o . . . . |  3 |  3   0 |  * 32   *   * | 1  0  6   0  0 |  6   0  12   0 0 | 12  0  8  0 |  8 0 1
. x . x . . . |  4 |  2   2 |  *  * 288   * | 0  1  1   4  0 |  1   4   4   4 0 |  4  4  4  1 |  4 1 1
. . . x3o . . |  3 |  0   3 |  *  *   * 192 | 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 | 8  *  *   *  *   6   0   0   0 0 | 12  0  0  0 |  8 0 0
o3x . x . . .   6 |  6   3 |  2  0   3   0 | * 96  *   *  * |  1   4   0   0 0 |  4  4  0  0 |  4 1 0
. x3o x . . .   6 |  6   3 |  0  2   3   0 | *  * 96   *  * |  1   0   4   0 0 |  4  0  4  0 |  4 0 1
. x . x3o . .   6 |  3   6 |  0  0   3   2 | *  *  * 384  * |  0   1   1   2 0 |  1  2  2  1 |  2 1 1
. . . x3o3o .   4 |  0   6 |  0  0   0   4 | *  *  *   * 96 |  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 | 24   *   *   * * |  4  0  0  0 |  4 0 0
o3x . x3o . .   9 |  9   9 |  3  0   9   3 | 0  3  0   3  0 |  * 128   *   * * |  1  2  0  0 |  2 1 0
. x3o x3o . .   9 |  9   9 |  0  3   9   3 | 0  0  3   3  0 |  *   * 128   * * |  1  0  2  0 |  2 0 1
. x . x3o3o .   8 |  4  12 |  0  0   6   8 | 0  0  0   4  2 |  *   *   * 192 * |  0  1  1  1 |  1 1 1
. . . x3o3o4o   8 |  0  24 |  0  0   0  32 | 0  0  0   0 16 |  *   *   *   * 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 | 32  *  *  * |  2 0 0
o3x . x3o3o .  12 | 12  18 |  4  0  18  12 | 0  6  0  12  3 |  0   4   0   3 0 |  * 64  *  * |  1 1 0
. x3o x3o3o .  12 | 12  18 |  0  4  18  12 | 0  0  6  12  3 |  0   0   4   3 0 |  *  * 64  * |  1 0 1
. x . x3o3o4o  16 |  8  48 |  0  0  24  64 | 0  0  0  32 32 |  0   0   0  16 2 |  *  *  * 12 |  0 1 1
--------------+----+--------+---------------+----------------+------------------+-------------+-------
o3x3o x3o3o .  24 | 48  48 | 16 16  72  24 | 4 24 24  48  6 |  6  16  16  12 0 |  4  4  4  0 | 16 * *
o3x . x3o3o4o  24 | 24  72 |  8  0  72  96 | 0 24  0  96 48 |  0  32   0  48 3 |  0 16  0  3 |  * 4 *
. x3o x3o3o4o  24 | 24  72 |  0  8  72  96 | 0  0 24  96 48 |  0   0  32  48 3 |  0  0 16  3 |  * * 4

x3o4o x3o3o *e3o

o3o4o o3o3o *e3o | 48 |  4   6 |  4  24  12 | 1  24  48  4  4 |  6  48 16 16 1 | 12 16 16  4 | 4 4 4
-----------------+----+--------+------------+-----------------+----------------+-------------+------
x . . . . .    . |  2 | 96   * |  2   6   0 | 1  12  12  0  0 |  6  24  4  4 0 | 12  8  8  1 | 4 4 2
. . . x . .    . |  2 |  * 144 |  0   4   4 | 0   4  16  2  2 |  1  16  8  8 1 |  4  8  8  4 | 2 2 4
-----------------+----+--------+------------+-----------------+----------------+-------------+------
x3o . . . .    . |  3 |  3   0 | 64   *   * | 1   6   0  0  0 |  6  12  0  0 0 | 12  4  4  0 | 4 4 1
x . . x . .    . |  4 |  2   2 |  * 288   * | 0   2   4  0  0 |  1   8  2  2 0 |  4  4  4  1 | 2 2 2
. . . x3o .    . |  3 |  0   3 |  *   * 192 | 0   0   4  1  1 |  0   4  4  4 1 |  1  4  4  4 | 1 1 4
-----------------+----+--------+------------+-----------------+----------------+-------------+------
x3o4o . . .    .   6 | 12   0 |  8   0   0 | 8   *   *  *  *   6   0  0  0 0 | 12  0  0  0 | 4 4 0
x3o . x . .    .   6 |  6   3 |  2   3   0 | * 192   *  *  * |  1   4  0  0 0 |  4  2  2  0 | 2 2 1
x . . x3o .    .   6 |  3   6 |  0   3   2 | *   * 384  *  * |  0   2  1  1 0 |  1  2  2  1 | 1 1 2
. . . x3o3o    .   4 |  0   6 |  0   0   4 | *   *   * 48  * |  0   0  4  0 1 |  0  4  0  4 | 1 0 4
. . . x3o . *e3o   4 |  0   6 |  0   0   4 | *   *   *  * 48 |  0   0  0  4 1 |  0  0  4  4 | 0 1 4
-----------------+----+--------+------------+-----------------+----------------+-------------+------
x3o4o x . .    .  12 | 24   6 | 16  12   0 | 2   8   0  0  0 | 24   *  *  * * |  4  0  0  0 | 2 2 0
x3o . x3o .    .   9 |  9   9 |  3   9   3 | 0   3   3  0  0 |  * 256  *  * * |  1  1  1  0 | 1 1 1
x . . x3o3o    .   8 |  4  12 |  0   6   8 | 0   0   4  2  0 |  *   * 96  * * |  0  2  0  1 | 1 0 2
x . . x3o . *e3o   8 |  4  12 |  0   6   8 | 0   0   4  0  2 |  *   *  * 96 * |  0  0  2  1 | 0 1 2
. . . x3o3o *e3o   8 |  0  24 |  0   0  32 | 0   0   0  8  8 |  *   *  *  * 6 |  0  0  0  4 | 0 0 4
-----------------+----+--------+------------+-----------------+----------------+-------------+------
x3o4o x3o .    .  18 | 36  18 | 24  36   6 | 3  24  12  0  0 |  3   8  0  0 0 | 32  *  *  * | 1 1 0
x3o . x3o3o    .  12 | 12  18 |  4  18  12 | 0   6  12  3  0 |  0   4  3  0 0 |  * 64  *  * | 1 0 1
x3o . x3o . *e3o  12 | 12  18 |  4  18  12 | 0   6  12  0  3 |  0   4  0  3 0 |  *  * 64  * | 0 1 1
x . . x3o3o *e3o  16 |  8  48 |  0  24  64 | 0   0  32 16 16 |  0   0  8  8 2 |  *  *  * 12 | 0 0 2
-----------------+----+--------+------------+-----------------+----------------+-------------+------
x3o4o x3o3o    .  24 | 48  48 | 32  72  24 | 4  48  48  6  0 |  6  32 12  0 0 |  4  8  0  0 | 8 * *
x3o4o x3o . *e3o  24 | 48  48 | 32  72  24 | 4  48  48  0  6 |  6  32  0 12 0 |  4  0  8  0 | * 8 *
x3o . x3o3o *e3o  24 | 24  72 |  8  72  96 | 0  24  96 24 24 |  0  32 24 24 3 |  0  8  8  3 | * * 8

o3x3o x3o3o *e3o

o3o3o o3o3o *e3o | 48 |  4   6 |  2  2  24  12 | 1 12 12  48  4  4 |  6  24  24 16 16 1 | 12  8  8  8  8  4 | 4 4 2 2
-----------------+----+--------+---------------+-------------------+--------------------+-------------------+--------
. x . . . .    . |  2 | 96   * |  1  1   6   0 | 1  6  6  12  0  0 |  6  12  12  4  4 0 | 12  4  4  4  4  1 | 4 4 1 1
. . . x . .    . |  2 |  * 144 |  0  0   4   4 | 0  2  2  16  2  2 |  1   8   8  8  8 1 |  4  4  4  4  4  4 | 2 2 2 2
-----------------+----+--------+---------------+-------------------+--------------------+-------------------+--------
o3x . . . .    . |  3 |  3   0 | 32  *   *   * | 1  6  0   0  0  0 |  6  12   0  0  0 0 | 12  4  4  0  0  0 | 4 4 1 0
. x3o . . .    . |  3 |  3   0 |  * 32   *   * | 1  0  6   0  0  0 |  6   0  12  0  0 0 | 12  0  0  4  4  0 | 4 4 0 1
. x . x . .    . |  4 |  2   2 |  *  * 288   * | 0  1  1   4  0  0 |  1   4   4  2  2 0 |  4  2  2  2  2  1 | 2 2 1 1
. . . x3o .    . |  3 |  0   3 |  *  *   * 192 | 0  0  0   4  1  1 |  0   2   2  4  4 1 |  1  2  2  2  2  4 | 1 1 2 2
-----------------+----+--------+---------------+-------------------+--------------------+-------------------+--------
o3x3o . . .    .   6 | 12   0 |  4  4   0   0 | 8  *  *   *  *  *   6   0   0  0  0 0 | 12  0  0  0  0  0 | 4 4 0 0
o3x . x . .    .   6 |  6   3 |  2  0   3   0 | * 96  *   *  *  * |  1   4   0  0  0 0 |  4  2  2  0  0  0 | 2 2 1 0
. x3o x . .    .   6 |  6   3 |  0  2   3   0 | *  * 96   *  *  * |  1   0   4  0  0 0 |  4  0  0  2  2  0 | 2 2 0 1
. x . x3o .    .   6 |  3   6 |  0  0   3   2 | *  *  * 384  *  * |  0   1   1  1  1 0 |  1  1  1  1  1  1 | 1 1 1 1
. . . x3o3o    .   4 |  0   6 |  0  0   0   4 | *  *  *   * 48  * |  0   0   0  4  0 1 |  0  2  0  2  0  4 | 1 0 2 2
. . . x3o . *e3o   4 |  0   6 |  0  0   0   4 | *  *  *   *  * 48 |  0   0   0  0  4 1 |  0  0  2  0  2  4 | 0 1 2 2
-----------------+----+--------+---------------+-------------------+--------------------+-------------------+--------
o3x3o x . .    .  12 | 24   6 |  8  8  12   0 | 2  4  4   0  0  0 | 24   *   *  *  * * |  4  0  0  0  0  0 | 2 2 0 0
o3x . x3o .    .   9 |  9   9 |  3  0   9   3 | 0  3  0   3  0  0 |  * 128   *  *  * * |  1  1  1  0  0  0 | 1 1 1 0
. x3o x3o .    .   9 |  9   9 |  0  3   9   3 | 0  0  3   3  0  0 |  *   * 128  *  * * |  1  0  0  1  1  0 | 1 1 0 1
. x . x3o3o    .   8 |  4  12 |  0  0   6   8 | 0  0  0   4  2  0 |  *   *   * 96  * * |  0  1  0  1  0  1 | 1 0 1 1
. x . x3o . *e3o   8 |  4  12 |  0  0   6   8 | 0  0  0   4  0  2 |  *   *   *  * 96 * |  0  0  1  0  1  1 | 0 1 1 1
. . . x3o3o *e3o   8 |  0  24 |  0  0   0  32 | 0  0  0   0  8  8 |  *   *   *  *  * 6 |  0  0  0  0  0  4 | 0 0 2 2
-----------------+----+--------+---------------+-------------------+--------------------+-------------------+--------
o3x3o x3o .    .  18 | 36  18 | 12 12  36   6 | 3 12 12  12  0  0 |  3   4   4  0  0 0 | 32  *  *  *  *  * | 1 1 0 0
o3x . x3o3o    .  12 | 12  18 |  4  0  18  12 | 0  6  0  12  3  0 |  0   4   0  3  0 0 |  * 32  *  *  *  * | 1 0 1 0
o3x . x3o . *e3o  12 | 12  18 |  4  0  18  12 | 0  6  0  12  0  3 |  0   4   0  0  3 0 |  *  * 32  *  *  * | 0 1 1 0
. x3o x3o3o    .  12 | 12  18 |  0  4  18  12 | 0  0  6  12  3  0 |  0   0   4  3  0 0 |  *  *  * 32  *  * | 1 0 0 1
. x3o x3o . *e3o  12 | 12  18 |  0  4  18  12 | 0  0  6  12  0  3 |  0   0   4  0  3 0 |  *  *  *  * 32  * | 0 1 0 1
. x . x3o3o *e3o  16 |  8  48 |  0  0  24  64 | 0  0  0  32 16 16 |  0   0   0  8  8 2 |  *  *  *  *  * 12 | 0 0 1 1
-----------------+----+--------+---------------+-------------------+--------------------+-------------------+--------
o3x3o x3o3o    .  24 | 48  48 | 16 16  72  24 | 4 24 24  48  6  0 |  6  16  16 12  0 0 |  4  4  0  4  0  0 | 8 * * *
o3x3o x3o . *e3o  24 | 48  48 | 16 16  72  24 | 4 24 24  48  0  6 |  6  16  16  0 12 0 |  4  0  4  0  4  0 | * 8 * *
o3x . x3o3o *e3o  24 | 24  72 |  8  0  72  96 | 0 24  0  96 24 24 |  0  32   0 24 24 3 |  0  8  8  0  0  3 | * * 4 *
. x3o x3o3o *e3o  24 | 24  72 |  0  8  72  96 | 0  0 24  96 24 24 |  0   0  32 24 24 3 |  0  0  0  8  8  3 | * * * 4

© 2004-2019
top of page