Acronym steth Name small tesseractitesseractihexadecachoron Cross sections ` ©` Circumradius sqrt[(3+sqrt(2))/2] = 1.485633 Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign General of army sidpith Colonel of regiment sidpith Externallinks

As abstract polytope steth is isomorphic to gittith, thereby replacing octagons by octagrams, resp. socco by gocco. – As such steth is a lieutenant.

Incidence matrix according to Dynkin symbol

```o3o3x4x4/3*b

. . . .      | 64 |  3  3 |  3  3  3 |  1 1 3
-------------+----+-------+----------+-------
. . x .      |  2 | 96  * |  2  0  1 |  1 0 2
. . . x      |  2 |  * 96 |  0  2  1 |  0 1 2
-------------+----+-------+----------+-------
. o3x .      |  3 |  3  0 | 64  *  * |  1 0 1
. o . x4/3*b |  4 |  0  4 |  * 48  * |  0 1 1
. . x4x      |  8 |  4  4 |  *  * 24 |  0 0 2
-------------+----+-------+----------+-------
o3o3x .      ♦  4 |  6  0 |  4  0  0 | 16 * *
o3o . x4/3*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
. o3x4x4/3*b ♦ 24 | 24 24 |  8  6  6 |  * * 8
```

```o3o3/2x4x4*b

. .   . .    | 64 |  3  3 |  3  3  3 |  1 1 3
-------------+----+-------+----------+-------
. .   x .    |  2 | 96  * |  2  0  1 |  1 0 2
. .   . x    |  2 |  * 96 |  0  2  1 |  0 1 2
-------------+----+-------+----------+-------
. o3/2x .    |  3 |  3  0 | 64  *  * |  1 0 1
. o   . x4*b |  4 |  0  4 |  * 48  * |  0 1 1
. .   x4x    |  8 |  4  4 |  *  * 24 |  0 0 2
-------------+----+-------+----------+-------
o3o3/2x .    ♦  4 |  6  0 |  4  0  0 | 16 * *
o3o   . x4*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
. o3/2x4x4*b ♦ 24 | 24 24 |  8  6  6 |  * * 8
```

```o3/2o3x4x4/3*b

.   . . .      | 64 |  3  3 |  3  3  3 |  1 1 3
---------------+----+-------+----------+-------
.   . x .      |  2 | 96  * |  2  0  1 |  1 0 2
.   . . x      |  2 |  * 96 |  0  2  1 |  0 1 2
---------------+----+-------+----------+-------
.   o3x .      |  3 |  3  0 | 64  *  * |  1 0 1
.   o . x4/3*b |  4 |  0  4 |  * 48  * |  0 1 1
.   . x4x      |  8 |  4  4 |  *  * 24 |  0 0 2
---------------+----+-------+----------+-------
o3/2o3x .      ♦  4 |  6  0 |  4  0  0 | 16 * *
o3/2o . x4/3*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
.   o3x4x4/3*b ♦ 24 | 24 24 |  8  6  6 |  * * 8
```

```o3/2o3/2x4x4*b

.   .   . .    | 64 |  3  3 |  3  3  3 |  1 1 3
---------------+----+-------+----------+-------
.   .   x .    |  2 | 96  * |  2  0  1 |  1 0 2
.   .   . x    |  2 |  * 96 |  0  2  1 |  0 1 2
---------------+----+-------+----------+-------
.   o3/2x .    |  3 |  3  0 | 64  *  * |  1 0 1
.   o   . x4*b |  4 |  0  4 |  * 48  * |  0 1 1
.   .   x4x    |  8 |  4  4 |  *  * 24 |  0 0 2
---------------+----+-------+----------+-------
o3/2o3/2x .    ♦  4 |  6  0 |  4  0  0 | 16 * *
o3/2o   . x4*b ♦  8 |  0 12 |  0  6  0 |  * 8 *
.   o3/2x4x4*b ♦ 24 | 24 24 |  8  6  6 |  * * 8
```