Acronym octhix
Name (octahedron, hexateron)-duoprism,
vertex figure of tarn
Circumradius sqrt(11/12) = 0.957427
Volume sqrt(6)/1440 = 0.00170103
Face vector 36, 162, 348, 456, 391, 218, 75, 14
Confer
general polytopal classes:
Wythoffian polyzetta   segmentozetta  

Incidence matrix according to Dynkin symbol

x3o4o x3o3o3o3o

. . . . . . . . | 36 |  4  5 |  4  20  10 | 1  20  40 10 |  5  40  40  5 | 10  40 20 1 | 10 20  4 | 5 4
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x . . . . . . . |  2 | 72  * |  2   5   0 | 1  10  10  0 |  5  20  10  0 | 10  20  5 0 | 10 10  1 | 5 2
. . . x . . . . |  2 |  * 90 |  0   4   4 | 0   4  16  6 |  1  16  24  4 |  4  24 16 1 |  6 16  4 | 4 4
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x3o . . . . . . |  3 |  3  0 | 48   *   * | 1   5   0  0 |  5  10   0  0 | 10  10  0 0 | 10  5  0 | 5 1
x . . x . . . . |  4 |  2  2 |  * 180   * | 0   2   4  0 |  1   8   6  0 |  4  12  4 0 |  6  8  1 | 4 2
. . . x3o . . . |  3 |  0  3 |  *   * 120 | 0   0   4  3 |  0   4  12  3 |  1  12 12 1 |  3 12  4 | 3 4
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x3o4o . . . . .   6 | 12  0 |  8   0   0 | 6   *   *  *   5   0   0  0 | 10   0  0 0 | 10  0  0 | 5 0
x3o . x . . . .   6 |  6  3 |  2   3   0 | * 120   *  * |  1   4   0  0 |  4   6  0 0 |  6  4  0 | 4 1
x . . x3o . . .   6 |  3  6 |  0   3   2 | *   * 240  * |  0   2   3  0 |  1   6  3 0 |  3  6  1 | 3 2
. . . x3o3o . .   4 |  0  6 |  0   0   4 | *   *   * 90 |  0   0   4  2 |  0   4  8 1 |  1  8  4 | 2 4
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x3o4o x . . . .  12 | 24  6 | 16  12   0 | 2   8   0  0 | 15   *   *  *   4   0  0 0 |  6  0  0 | 4 0
x3o . x3o . . .   9 |  9  9 |  3   9   3 | 0   3   3  0 |  * 160   *  * |  1   3  0 0 |  3  3  0 | 3 1
x . . x3o3o . .   8 |  4 12 |  0   6   8 | 0   0   4  2 |  *   * 180  * |  0   2  2 0 |  1  4  1 | 2 2
. . . x3o3o3o .   5 |  0 10 |  0   0  10 | 0   0   0  5 |  *   *   * 36 |  0   0  4 1 |  0  4  4 | 1 4
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x3o4o x3o . . .  18 | 36 18 | 24  36   6 | 3  24  12  0 |  3   8   0  0 | 20   *  * * |  3  0  0 | 3 0
x3o . x3o3o . .  12 | 12 18 |  4  18  12 | 0   6  12  3 |  0   4   3  0 |  * 120  * * |  1  2  0 | 2 1
x . . x3o3o3o .  10 |  5 20 |  0  10  20 | 0   0  10 10 |  0   0   5  2 |  *   * 72 * |  0  2  1 | 1 2
. . . x3o3o3o3o   6 |  0 15 |  0   0  20 | 0   0   0 15 |  0   0   0  6 |  *   *  * 6 |  0  0  4 | 0 4
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x3o4o x3o3o . .  24 | 48 36 | 32  72  24 | 4  48  48  6 |  6  32  12  0 |  4   8  0 0 | 15  *  * | 2 0
x3o . x3o3o3o .  15 | 15 30 |  5  30  30 | 0  10  30 15 |  0  10  15  3 |  0   5  3 0 |  * 48  * | 1 1
x . . x3o3o3o3o  12 |  6 30 |  0  15  40 | 0   0  20 30 |  0   0  15 12 |  0   0  6 2 |  *  * 12 | 0 2
----------------+----+-------+------------+--------------+---------------+-------------+----------+----
x3o4o x3o3o3o .  30 | 60 60 | 40 120  60 | 5  80 120 30 | 10  80  60  6 | 10  40 12 0 |  5  8  0 | 6 *
x3o . x3o3o3o3o  18 | 18 45 |  6  45  60 | 0  15  60 45 |  0  20  45 18 |  0  15 18 3 |  0  6  3 | * 8

o3x3o x3o3o3o3o

. . . . . . . . | 36 |  4  5 |  2  2  20  10 | 1 10 10  40 10 |  5 20 20  40  5 | 10 20 20 20 1 | 10 10 10  4 | 5 2 2
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
. x . . . . . . |  2 | 72  * |  1  1   5   0 | 1  5  5  10  0 |  5 10 10  10  0 | 10 10 10  5 0 | 10  5  5  1 | 5 1 1
. . . x . . . . |  2 |  * 90 |  0  0   4   4 | 0  2  2  16  6 |  1  8  8  24  4 |  4 12 12 16 1 |  6  8  8  4 | 4 2 2
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
o3x . . . . . . |  3 |  3  0 | 24  *   *   * | 1  5  0   0  0 |  5 10  0   0  0 | 10 10  0  0 0 | 10  5  0  0 | 5 1 0
. x3o . . . . . |  3 |  3  0 |  * 24   *   * | 1  0  5   0  0 |  5  0 10   0  0 | 10  0 10  0 0 | 10  0  5  0 | 5 0 1
. x . x . . . . |  4 |  2  2 |  *  * 180   * | 0  1  1   4  0 |  1  4  4   6  0 |  4  6  6  4 0 |  6  4  4  1 | 4 1 1
. . . x3o . . . |  3 |  0  3 |  *  *   * 120 | 0  0  0   4  3 |  0  2  2  12  3 |  1  6  6 12 1 |  3  6  6  4 | 3 2 2
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
o3x3o . . . . .   6 | 12  0 |  4  4   0   0 | 6  *  *   *  *   5  0  0   0  0 | 10  0  0  0 0 | 10  0  0  0 | 5 0 0
o3x . x . . . .   6 |  6  3 |  2  0   3   0 | * 60  *   *  * |  1  4  0   0  0 |  4  6  0  0 0 |  6  4  0  0 | 4 1 0
. x3o x . . . .   6 |  6  3 |  0  2   3   0 | *  * 60   *  * |  1  0  4   0  0 |  4  0  6  0 0 |  6  0  4  0 | 4 0 1
. x . x3o . . .   6 |  3  6 |  0  0   3   2 | *  *  * 240  * |  0  1  1   3  0 |  1  3  3  3 0 |  3  3  3  1 | 3 1 1
. . . x3o3o . .   4 |  0  6 |  0  0   0   4 | *  *  *   * 90 |  0  0  0   4  2 |  0  2  2  8 1 |  1  4  4  4 | 2 2 2
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
o3x3o x . . . .  12 | 24  6 |  8  8  12   0 | 2  4  4   0  0 | 15  *  *   *  *   4  0  0  0 0 |  6  0  0  0 | 4 0 0
o3x . x3o . . .   9 |  9  9 |  3  0   9   3 | 0  3  0   3  0 |  * 80  *   *  * |  1  3  0  0 0 |  3  3  0  0 | 3 1 0
. x3o x3o . . .   9 |  9  9 |  0  3   9   3 | 0  0  3   3  0 |  *  * 80   *  * |  1  0  3  0 0 |  3  0  3  0 | 3 0 1
. x . x3o3o . .   8 |  4 12 |  0  0   6   8 | 0  0  0   4  2 |  *  *  * 180  * |  0  1  1  2 0 |  1  2  2  1 | 2 1 1
. . . x3o3o3o .   5 |  0 10 |  0  0   0  10 | 0  0  0   0  5 |  *  *  *   * 36 |  0  0  0  4 1 |  0  2  2  4 | 1 2 2
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
o3x3o x3o . . .  18 | 36 18 | 12 12  36   6 | 3 12 12  12  0 |  3  4  4   0  0 | 20  *  *  * * |  3  0  0  0 | 3 0 0
o3x . x3o3o . .  12 | 12 18 |  4  0  18  12 | 0  6  0  12  3 |  0  4  0   3  0 |  * 60  *  * * |  1  2  0  0 | 2 1 0
. x3o x3o3o . .  12 | 12 18 |  0  4  18  12 | 0  0  6  12  3 |  0  0  4   3  0 |  *  * 60  * * |  1  0  2  0 | 2 0 1
. x . x3o3o3o .  10 |  5 20 |  0  0  10  20 | 0  0  0  10 10 |  0  0  0   5  2 |  *  *  * 72 * |  0  1  1  1 | 1 1 1
. . . x3o3o3o3o   6 |  0 15 |  0  0   0  20 | 0  0  0   0 15 |  0  0  0   0  6 |  *  *  *  * 6 |  0  0  0  4 | 0 2 2
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
o3x3o x3o3o . .  24 | 48 36 | 16 16  72  24 | 4 24 24  48  6 |  6 16 16  12  0 |  4  4  4  0 0 | 15  *  *  * | 2 0 0
o3x . x3o3o3o .  15 | 15 30 |  5  0  30  30 | 0 10  0  30 15 |  0 10  0  15  3 |  0  5  0  3 0 |  * 24  *  * | 1 1 0
. x3o x3o3o3o .  15 | 15 30 |  0  5  30  30 | 0  0 10  30 15 |  0  0 10  15  3 |  0  0  5  3 0 |  *  * 24  * | 1 0 1
. x . x3o3o3o3o  12 |  6 30 |  0  0  15  40 | 0  0  0  20 30 |  0  0  0  15 12 |  0  0  0  6 2 |  *  *  * 12 | 0 1 1
----------------+----+-------+---------------+----------------+-----------------+---------------+-------------+------
o3x3o x3o3o3o .  30 | 60 60 | 20 20 120  60 | 5 40 40 120 30 | 10 40 40  60  6 | 10 20 20 12 0 |  5  4  4  0 | 6 * *
o3x . x3o3o3o3o  18 | 18 45 |  6  0  45  60 | 0 15  0  60 45 |  0 20  0  45 18 |  0 15  0 18 3 |  0  6  0  3 | * 4 *
. x3o x3o3o3o3o  18 | 18 45 |  0  6  45  60 | 0  0 15  60 45 |  0  0 20  45 18 |  0  0 15 18 3 |  0  0  6  3 | * * 4

ox3oo3oo3oo xx3oo4oo&#x   → height = sqrt(3/5) = 0.774597

... 

xo ox3oo3oo xx3oo4oo&#x   → height = sqrt(3/8) = 0.612372

... 

xo3oo ox3oo xx3oo4oo&#x   → height = 1/sqrt(3) = 0.577350

... 

ox3oo3oo3oo oo3xx3oo&#x   → height = sqrt(3/5) = 0.774597

... 

xo ox3oo3oo oo3xx3oo&#x   → height = sqrt(3/8) = 0.612372

... 

xo3oo ox3oo oo3xx3oo&#x   → height = 1/sqrt(3) = 0.577350

... 

xo3ox xx3oo3oo3oo3oo&#x   → height = 1/sqrt(2) = 0.707107

... 

© 2004-2025
top of page