Acronym hept
Name hepteract,
7D measure-polytope7),
geozett(id)
|,>,O device line prism prism prism prism prism prism = |||||||
Vertex layers
 Layer Symmetry Subsymmetries o3o3o3o3o3o4o o3o3o3o3o3o . . o3o3o3o3o4o 1 o3o3o3o3o3o4x o3o3o3o3o3o .vertex first . o3o3o3o3o4xax first 2 o3o3o3o3o3q .vertex figure . o3o3o3o3o4xopposite ax 3 o3o3o3o3q3o . 4 o3o3o3q3o3o . 5 o3o3q3o3o3o . 6 o3q3o3o3o3o . 7 q3o3o3o3o3o . 8 o3o3o3o3o3o .opposite vertex
Coordinates (1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all changes of sign
Volume 1
Surface 14
Rel. Roundness π3/840 = 3.691223 %
Dual zee
Dihedral angles
Confer
general triprism-prisms:
n,n,n-tippip
general polytopal classes:
hypercube   noble polytopes   segmentoexa
analogs:
regular hypercube Cn
External

Its equatorial cross-section in vertex first orientation is not a vertex layer. Even so it can be determined as 1/q-fe (cf. truncation series).

Incidence matrix according to Dynkin symbol

```o3o3o3o3o3o4x

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

snubbed forms: o3o3o3o3o3o4s
```

```x o3o3o3o3o4x

. . . . . . . | 128 ♦  1   6 |   6  15 |  15  20 |  20  15 | 15  6 |  6 1
--------------+-----+--------+---------+---------+---------+-------+-----
x . . . . . . |   2 | 64   * ♦   6   0 |  15   0 |  20   0 | 15  0 |  6 0
. . . . . . x |   2 |  * 384 ♦   1   5 |   5  10 |  10  10 | 10  5 |  5 1
--------------+-----+--------+---------+---------+---------+-------+-----
x . . . . . x |   4 |  2   2 | 192   * ♦   5   0 |  10   0 | 10  0 |  5 0
. . . . . o4x |   4 |  0   4 |   * 480 ♦   1   4 |   4   6 |  6  4 |  4 1
--------------+-----+--------+---------+---------+---------+-------+-----
x . . . . o4x ♦   8 |  4   8 |   4   2 | 240   * ♦   4   0 |  6  0 |  4 0
. . . . o3o4x ♦   8 |  0  12 |   0   6 |   * 320 ♦   1   3 |  3  3 |  3 1
--------------+-----+--------+---------+---------+---------+-------+-----
x . . . o3o4x ♦  16 |  8  24 |  12  12 |   6   2 | 160   * |  3  0 |  3 0
. . . o3o3o4x ♦  16 |  0  32 |   0  24 |   0   8 |   * 120 |  1  2 |  2 1
--------------+-----+--------+---------+---------+---------+-------+-----
x . . o3o3o4x ♦  32 | 16  64 |  32  48 |  24  16 |   8   2 | 60  * |  2 0
. . o3o3o3o4x ♦  32 |  0  80 |   0  80 |   0  40 |   0  10 |  * 24 |  1 1
--------------+-----+--------+---------+---------+---------+-------+-----
x . o3o3o3o4x ♦  64 | 32 160 |  80 160 |  80  80 |  40  20 | 10  2 | 12 *
. o3o3o3o3o4x ♦  64 |  0 192 |   0 240 |   0 160 |   0  60 |  0 12 |  * 2
```

```o4x o3o3o3o4x

. . . . . . . | 128 ♦   2   5 |  1  10  10 |  5  20  10 | 10  20  5 | 10 10 1 |  5 2
--------------+-----+---------+------------+------------+-----------+---------+-----
. x . . . . . |   2 | 128   * ♦  1   5   0 |  5  10   0 | 10  10  0 | 10  5 0 |  5 1
. . . . . . x |   2 |   * 320 ♦  0   2   4 |  1   8   6 |  4  12  4 |  6  8 1 |  4 2
--------------+-----+---------+------------+------------+-----------+---------+-----
o4x . . . . . |   4 |   4   0 | 32   *   * ♦  5   0   0 | 10   0  0 | 10  0 0 |  5 0
. x . . . . x |   4 |   2   2 |  * 320   * ♦  1   4   0 |  4   6  0 |  6  4 0 |  4 1
. . . . . o4x |   4 |   0   4 |  *   * 320 ♦  0   2   3 |  1   6  3 |  3  6 1 |  3 2
--------------+-----+---------+------------+------------+-----------+---------+-----
o4x . . . . x ♦   8 |   8   4 |  2   4   0 | 80   *   * ♦  4   0  0 |  6  0 0 |  4 0
. x . . . o4x ♦   8 |   4   8 |  0   4   2 |  * 320   * ♦  1   3  0 |  3  3 0 |  3 1
. . . . o3o4x ♦   8 |   0  12 |  0   0   6 |  *   * 160 ♦  0   2  2 |  1  4 1 |  2 2
--------------+-----+---------+------------+------------+-----------+---------+-----
o4x . . . o4x ♦  16 |  16  16 |  4  16   4 |  4   4   0 | 80   *  * |  3  0 0 |  3 0
. x . . o3o4x ♦  16 |   8  24 |  0  12  12 |  0   6   2 |  * 160  * |  1  2 0 |  2 1
. . . o3o3o4x ♦  16 |   0  32 |  0   0  24 |  0   0   8 |  *   * 40 |  0  2 1 |  1 2
--------------+-----+---------+------------+------------+-----------+---------+-----
o4x . . o3o4x ♦  32 |  32  48 |  8  48  24 | 12  24   4 |  6   4  0 | 40  * * |  2 0
. x . o3o3o4x ♦  32 |  16  64 |  0  32  48 |  0  24  16 |  0   8  2 |  * 40 * |  1 1
. . o3o3o3o4x ♦  32 |   0  80 |  0   0  80 |  0   0  40 |  0   0 10 |  *  * 4 |  0 2
--------------+-----+---------+------------+------------+-----------+---------+-----
o4x . o3o3o4x ♦  64 |  64 128 | 16 128  96 | 36  96  32 | 24  32  4 |  8  4 0 | 10 *
. x o3o3o3o4x ♦  64 |  32 160 |  0  80 160 |  0  80  80 |  0  40 20 |  0 10 2 |  * 4
```

```o3o4x o3o3o4x

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

```oo3oo3oo3oo3oo4xx&#x   → height = 1
(ax || ax)

o.3o.3o.3o.3o.4o.    & | 128 ♦   6  1 |  15   6 |  20  15 |  15  20 |  6 15 | 1  6
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. .. .. .. x.    & |   2 | 384  * ♦   5   1 |  10   5 |  10  10 |  5 10 | 1  5
oo3oo3oo3oo3oo4oo&#x   |   2 |   * 64 ♦   0   6 |   0  15 |   0  20 |  0 15 | 0  6
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. .. .. o.4x.    & |   4 |   4  0 | 480   * ♦   4   1 |   6   4 |  4  6 | 1  4
.. .. .. .. .. xx&#x   |   4 |   2  2 |   * 192 ♦   0   5 |   0  10 |  0 10 | 0  5
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. .. o.3o.4x.    & ♦   8 |  12  0 |   6   0 | 320   * ♦   3   1 |  3  3 | 1  3
.. .. .. .. oo4xx&#x   ♦   8 |   8  4 |   2   4 |   * 240 ♦   0   4 |  0  6 | 0  4
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. o.3o.3o.4x.    & ♦  16 |  32  0 |  24   0 |   8   0 | 120   * |  2  1 | 1  2
.. .. .. oo3oo4xx&#x   ♦  16 |  24  8 |  12  12 |   2   6 |   * 160 |  0  3 | 0  3
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. o.3o.3o.3o.4x.    & ♦  32 |  80  0 |  80   0 |  40   0 |  10   0 | 24  * | 1  1
.. .. oo3oo3oo4xx&#x   ♦  32 |  64 16 |  48  32 |  16  24 |   2   8 |  * 60 | 0  2
-----------------------+-----+--------+---------+---------+---------+-------+-----
o.3o.3o.3o.3o.4x.    & ♦  64 | 192  0 | 240   0 | 160   0 |  60   0 | 12  0 | 2  *
.. oo3oo3oo3oo4xx&#x   ♦  64 | 160 32 | 160  80 |  80  80 |  20  40 |  2 10 | * 12
```