Acronym	octo
Name	octeract, hexadecazetton, 8D measure-polytope (γ8), geoyott(id)
Circumradius	sqrt(2) = 1.414214
Inradius	1/2
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o3o3o3o4o o3o3o3o3o3o3o . . o3o3o3o3o3o4o 1 o3o3o3o3o3o3o4x o3o3o3o3o3o3o . vertex first . o3o3o3o3o3o4x hept first 2 o3o3o3o3o3o3q . vertex figure . o3o3o3o3o3o4x opposite hept 3 o3o3o3o3o3q3o .   4 o3o3o3o3q3o3o . 5 o3o3o3q3o3o3o . 6 o3o3q3o3o3o3o . 7 o3q3o3o3o3o3o . 8 q3o3o3o3o3o3o . 9 o3o3o3o3o3o3o . opposite vertex
Coordinates	(1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all changes of sign
Volume	1
Surface	16
Rel. Roundness	π4/6144 = 1.585434 %
Dual	ek
Dihedral angles	at ax between hept and hept:   90°
Face vector	256, 1024, 1792, 1792, 1120, 448, 112, 16
Confer	general polytopal classes: Wythoffian polyzetta   hypercube   noble polytopes   segmentozetta   analogs: regular hypercube Cn
External links

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3o4x

. . . . . . . . | 256 ♦    8 |   28 |   56 |   70 |  56 |  28 |  8
----------------+-----+------+------+------+------+-----+-----+---
. . . . . . . x |   2 | 1024 ♦    7 |   21 |   35 |  35 |  21 |  7
----------------+-----+------+------+------+------+-----+-----+---
. . . . . . o4x |   4 |    4 | 1792 ♦    6 |   15 |  20 |  15 |  6
----------------+-----+------+------+------+------+-----+-----+---
. . . . . o3o4x ♦   8 |   12 |    6 | 1792 ♦    5 |  10 |  10 |  5
----------------+-----+------+------+------+------+-----+-----+---
. . . . o3o3o4x ♦  16 |   32 |   24 |    8 | 1120 ♦   4 |   6 |  4
----------------+-----+------+------+------+------+-----+-----+---
. . . o3o3o3o4x ♦  32 |   80 |   80 |   40 |   10 | 448 |   3 |  3
----------------+-----+------+------+------+------+-----+-----+---
. . o3o3o3o3o4x ♦  64 |  192 |  240 |  160 |   60 |  12 | 112 |  2
----------------+-----+------+------+------+------+-----+-----+---
. o3o3o3o3o3o4x ♦ 128 |  448 |  672 |  560 |  280 |  84 |  14 | 16

snubbed forms: o3o3o3o3o3o3o4s

o3o3o3o3o3o3o4/3x

. . . . . . .   . | 256 ♦    8 |   28 |   56 |   70 |  56 |  28 |  8
------------------+-----+------+------+------+------+-----+-----+---
. . . . . . .   x |   2 | 1024 ♦    7 |   21 |   35 |  35 |  21 |  7
------------------+-----+------+------+------+------+-----+-----+---
. . . . . . o4/3x |   4 |    4 | 1792 ♦    6 |   15 |  20 |  15 |  6
------------------+-----+------+------+------+------+-----+-----+---
. . . . . o3o4/3x ♦   8 |   12 |    6 | 1792 ♦    5 |  10 |  10 |  5
------------------+-----+------+------+------+------+-----+-----+---
. . . . o3o3o4/3x ♦  16 |   32 |   24 |    8 | 1120 ♦   4 |   6 |  4
------------------+-----+------+------+------+------+-----+-----+---
. . . o3o3o3o4/3x ♦  32 |   80 |   80 |   40 |   10 | 448 |   3 |  3
------------------+-----+------+------+------+------+-----+-----+---
. . o3o3o3o3o4/3x ♦  64 |  192 |  240 |  160 |   60 |  12 | 112 |  2
------------------+-----+------+------+------+------+-----+-----+---
. o3o3o3o3o3o4/3x ♦ 128 |  448 |  672 |  560 |  280 |  84 |  14 | 16

o3o3o4x o3o3o4x

. . . . . . . . | 256 ♦   4   4 |   6   16   6 |   4  24  24   4 |  1  16  36  16  1 |  4  24  24  4 |  6 16  6 | 4 4
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. . . x . . . . |   2 | 512   * ♦   3    4   0 |   3  12   6   0 |  1  12  18   4  0 |  4  18  12  1 |  6 12  3 | 4 3
. . . . . . . x |   2 |   * 512 ♦   0    4   3 |   0   6  12   3 |  0   4  18  12  1 |  1  12  18  4 |  3 12  6 | 3 4
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. . o4x . . . . |   4 |   4   0 | 384    *   * ♦   2   4   0   0 |  1   8   6   0  0 |  4  12   4  0 |  6  8  1 | 4 2
. . . x . . . x |   4 |   2   2 |   * 1024   * ♦   0   3   3   0 |  0   3   9   3  0 |  1   9   9  1 |  3  9  3 | 3 3
. . . . . . o4x |   4 |   0   4 |   *    * 384 ♦   0   0   4   2 |  0   0   6   8  1 |  0   4  12  4 |  1  8  6 | 2 4
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. o3o4x . . . . ♦   8 |  12   0 |   6    0   0 | 128   *   *   * ♦  1   4   0   0  0 |  4   6   0  0 |  6  4  0 | 4 0
. . o4x . . . x ♦   8 |   8   4 |   2    4   0 |   * 768   *   * ♦  0   2   3   0  0 |  1   6   3  0 |  3  6  1 | 3 2
. . . x . . o4x ♦   8 |   4   8 |   0    4   2 |   *   * 768   * ♦  0   0   3   2  0 |  0   3   6  1 |  1  6  3 | 2 3
. . . . . o3o4x ♦   8 |   0  12 |   0    0   6 |   *   *   * 128 ♦  0   0   0   4  1 |  0   0   6  4 |  0  4  6 | 1 4
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . . . . ♦  16 |  32   0 |  24    0   0 |   8   0   0   0 | 16   *   *   *  * ♦  4   0   0  0 |  6  0  0 | 4 0
. o3o4x . . . x ♦  16 |  24   8 |  12   12   0 |   2   6   0   0 |  * 256   *   *  * ♦  1   3   0  0 |  3  3  0 | 3 1
. . o4x . . o4x ♦  16 |  16  16 |   4   16   4 |   0   4   4   0 |  *   * 576   *  * ♦  0   2   2  0 |  1  4  1 | 2 2
. . . x . o3o4x ♦  16 |   8  24 |   0   12  12 |   0   0   6   2 |  *   *   * 256  * ♦  0   0   3  1 |  0  3  3 | 1 3
. . . . o3o3o4x ♦  16 |   0  32 |   0    0  24 |   0   0   0   8 |  *   *   *   * 16 ♦  0   0   0  4 |  0  0  6 | 0 4
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . . . x ♦  32 |  64  16 |  48   32   0 |  16  24   0   0 |  2   8   0   0  0 | 32   *   *  * |  3  0  0 | 3 0
. o3o4x . . o4x ♦  32 |  48  32 |  24   48   8 |   4  24  12   0 |  0   4   6   0  0 |  * 192   *  * |  1  2  0 | 2 1
. . o4x . o3o4x ♦  32 |  32  48 |   8   48  24 |   0  12  24   4 |  0   0   6   4  0 |  *   * 192  * |  0  2  1 | 1 2
. . . x o3o3o4x ♦  32 |  16  64 |   0   32  48 |   0   0  24  16 |  0   0   0   8  2 |  *   *   * 32 |  0  0  3 | 0 3
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . . o4x ♦  64 | 128  64 |  96  128  16 |  32  96  32   0 |  4  32  24   0  0 |  4   8   0  0 | 24  *  * | 2 0
. o3o4x . o3o4x ♦  64 |  96  96 |  48  144  48 |   8  72  72   8 |  0  12  36  12  0 |  0   6   6  0 |  * 64  * | 1 1
. . o4x o3o3o4x ♦  64 |  64 128 |  16  128  96 |   0  32  96  32 |  0   0  24  32  4 |  0   0   8  4 |  *  * 24 | 0 2
----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . o3o4x ♦ 128 | 256 192 | 192  384  96 |  64 288 192  16 |  8  96 144  32  0 | 12  48  24  0 |  6  8  0 | 8 *
. o3o4x o3o3o4x ♦ 128 | 192 256 |  96  384 192 |  16 192 288  64 |  0  32 144  96  8 |  0  24  48 12 |  0  8  6 | * 8

snubbed forms: o3o3o4s o3o3o4x

o3o3o4x o3o3o4/3x

. . . . . . .   . | 256 ♦   4   4 |   6   16   6 |   4  24  24   4 |  1  16  36  16  1 |  4  24  24  4 |  6 16  6 | 4 4
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. . . x . . .   . |   2 | 512   * ♦   3    4   0 |   3  12   6   0 |  1  12  18   4  0 |  4  18  12  1 |  6 12  3 | 4 3
. . . . . . .   x |   2 |   * 512 ♦   0    4   3 |   0   6  12   3 |  0   4  18  12  1 |  1  12  18  4 |  3 12  6 | 3 4
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. . o4x . . .   . |   4 |   4   0 | 384    *   * ♦   2   4   0   0 |  1   8   6   0  0 |  4  12   4  0 |  6  8  1 | 4 2
. . . x . . .   x |   4 |   2   2 |   * 1024   * ♦   0   3   3   0 |  0   3   9   3  0 |  1   9   9  1 |  3  9  3 | 3 3
. . . . . . o4/3x |   4 |   0   4 |   *    * 384 ♦   0   0   4   2 |  0   0   6   8  1 |  0   4  12  4 |  1  8  6 | 2 4
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. o3o4x . . .   . ♦   8 |  12   0 |   6    0   0 | 128   *   *   * ♦  1   4   0   0  0 |  4   6   0  0 |  6  4  0 | 4 0
. . o4x . . .   x ♦   8 |   8   4 |   2    4   0 |   * 768   *   * ♦  0   2   3   0  0 |  1   6   3  0 |  3  6  1 | 3 2
. . . x . . o4/3x ♦   8 |   4   8 |   0    4   2 |   *   * 768   * ♦  0   0   3   2  0 |  0   3   6  1 |  1  6  3 | 2 3
. . . . . o3o4/3x ♦   8 |   0  12 |   0    0   6 |   *   *   * 128 ♦  0   0   0   4  1 |  0   0   6  4 |  0  4  6 | 1 4
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . . .   . ♦  16 |  32   0 |  24    0   0 |   8   0   0   0 | 16   *   *   *  * ♦  4   0   0  0 |  6  0  0 | 4 0
. o3o4x . . .   x ♦  16 |  24   8 |  12   12   0 |   2   6   0   0 |  * 256   *   *  * ♦  1   3   0  0 |  3  3  0 | 3 1
. . o4x . . o4/3x ♦  16 |  16  16 |   4   16   4 |   0   4   4   0 |  *   * 576   *  * ♦  0   2   2  0 |  1  4  1 | 2 2
. . . x . o3o4/3x ♦  16 |   8  24 |   0   12  12 |   0   0   6   2 |  *   *   * 256  * ♦  0   0   3  1 |  0  3  3 | 1 3
. . . . o3o3o4/3x ♦  16 |   0  32 |   0    0  24 |   0   0   0   8 |  *   *   *   * 16 ♦  0   0   0  4 |  0  0  6 | 0 4
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . . .   x ♦  32 |  64  16 |  48   32   0 |  16  24   0   0 |  2   8   0   0  0 | 32   *   *  * |  3  0  0 | 3 0
. o3o4x . . o4/3x ♦  32 |  48  32 |  24   48   8 |   4  24  12   0 |  0   4   6   0  0 |  * 192   *  * |  1  2  0 | 2 1
. . o4x . o3o4/3x ♦  32 |  32  48 |   8   48  24 |   0  12  24   4 |  0   0   6   4  0 |  *   * 192  * |  0  2  1 | 1 2
. . . x o3o3o4/3x ♦  32 |  16  64 |   0   32  48 |   0   0  24  16 |  0   0   0   8  2 |  *   *   * 32 |  0  0  3 | 0 3
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . . o4/3x ♦  64 | 128  64 |  96  128  16 |  32  96  32   0 |  4  32  24   0  0 |  4   8   0  0 | 24  *  * | 2 0
. o3o4x . o3o4/3x ♦  64 |  96  96 |  48  144  48 |   8  72  72   8 |  0  12  36  12  0 |  0   6   6  0 |  * 64  * | 1 1
. . o4x o3o3o4/3x ♦  64 |  64 128 |  16  128  96 |   0  32  96  32 |  0   0  24  32  4 |  0   0   8  4 |  *  * 24 | 0 2
------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4x . o3o4/3x ♦ 128 | 256 192 | 192  384  96 |  64 288 192  16 |  8  96 144  32  0 | 12  48  24  0 |  6  8  0 | 8 *
. o3o4x o3o3o4/3x ♦ 128 | 192 256 |  96  384 192 |  16 192 288  64 |  0  32 144  96  8 |  0  24  48 12 |  0  8  6 | * 8

o3o3o4/3x o3o3o4/3x

. . .   . . . .   . | 256 ♦   4   4 |   6   16   6 |   4  24  24   4 |  1  16  36  16  1 |  4  24  24  4 |  6 16  6 | 4 4
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. . .   x . . .   . |   2 | 512   * ♦   3    4   0 |   3  12   6   0 |  1  12  18   4  0 |  4  18  12  1 |  6 12  3 | 4 3
. . .   . . . .   x |   2 |   * 512 ♦   0    4   3 |   0   6  12   3 |  0   4  18  12  1 |  1  12  18  4 |  3 12  6 | 3 4
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. . o4/3x . . .   . |   4 |   4   0 | 384    *   * ♦   2   4   0   0 |  1   8   6   0  0 |  4  12   4  0 |  6  8  1 | 4 2
. . .   x . . .   x |   4 |   2   2 |   * 1024   * ♦   0   3   3   0 |  0   3   9   3  0 |  1   9   9  1 |  3  9  3 | 3 3
. . .   . . . o4/3x |   4 |   0   4 |   *    * 384 ♦   0   0   4   2 |  0   0   6   8  1 |  0   4  12  4 |  1  8  6 | 2 4
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
. o3o4/3x . . .   . ♦   8 |  12   0 |   6    0   0 | 128   *   *   * ♦  1   4   0   0  0 |  4   6   0  0 |  6  4  0 | 4 0
. . o4/3x . . .   x ♦   8 |   8   4 |   2    4   0 |   * 768   *   * ♦  0   2   3   0  0 |  1   6   3  0 |  3  6  1 | 3 2
. . .   x . . o4/3x ♦   8 |   4   8 |   0    4   2 |   *   * 768   * ♦  0   0   3   2  0 |  0   3   6  1 |  1  6  3 | 2 3
. . .   . . o3o4/3x ♦   8 |   0  12 |   0    0   6 |   *   *   * 128 ♦  0   0   0   4  1 |  0   0   6  4 |  0  4  6 | 1 4
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4/3x . . .   . ♦  16 |  32   0 |  24    0   0 |   8   0   0   0 | 16   *   *   *  * ♦  4   0   0  0 |  6  0  0 | 4 0
. o3o4/3x . . .   x ♦  16 |  24   8 |  12   12   0 |   2   6   0   0 |  * 256   *   *  * ♦  1   3   0  0 |  3  3  0 | 3 1
. . o4/3x . . o4/3x ♦  16 |  16  16 |   4   16   4 |   0   4   4   0 |  *   * 576   *  * ♦  0   2   2  0 |  1  4  1 | 2 2
. . .   x . o3o4/3x ♦  16 |   8  24 |   0   12  12 |   0   0   6   2 |  *   *   * 256  * ♦  0   0   3  1 |  0  3  3 | 1 3
. . .   . o3o3o4/3x ♦  16 |   0  32 |   0    0  24 |   0   0   0   8 |  *   *   *   * 16 ♦  0   0   0  4 |  0  0  6 | 0 4
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4/3x . . .   x ♦  32 |  64  16 |  48   32   0 |  16  24   0   0 |  2   8   0   0  0 | 32   *   *  * |  3  0  0 | 3 0
. o3o4/3x . . o4/3x ♦  32 |  48  32 |  24   48   8 |   4  24  12   0 |  0   4   6   0  0 |  * 192   *  * |  1  2  0 | 2 1
. . o4/3x . o3o4/3x ♦  32 |  32  48 |   8   48  24 |   0  12  24   4 |  0   0   6   4  0 |  *   * 192  * |  0  2  1 | 1 2
. . .   x o3o3o4/3x ♦  32 |  16  64 |   0   32  48 |   0   0  24  16 |  0   0   0   8  2 |  *   *   * 32 |  0  0  3 | 0 3
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4/3x . . o4/3x ♦  64 | 128  64 |  96  128  16 |  32  96  32   0 |  4  32  24   0  0 |  4   8   0  0 | 24  *  * | 2 0
. o3o4/3x . o3o4/3x ♦  64 |  96  96 |  48  144  48 |   8  72  72   8 |  0  12  36  12  0 |  0   6   6  0 |  * 64  * | 1 1
. . o4/3x o3o3o4/3x ♦  64 |  64 128 |  16  128  96 |   0  32  96  32 |  0   0  24  32  4 |  0   0   8  4 |  *  * 24 | 0 2
--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----
o3o3o4/3x . o3o4/3x ♦ 128 | 256 192 | 192  384  96 |  64 288 192  16 |  8  96 144  32  0 | 12  48  24  0 |  6  8  0 | 8 *
. o3o4/3x o3o3o4/3x ♦ 128 | 192 256 |  96  384 192 |  16 192 288  64 |  0  32 144  96  8 |  0  24  48 12 |  0  8  6 | * 8