Acronym rawvatoth Name retrosphenoverted tesseractitesseractihexadacachoron Cross sections ` ©` Circumradius sqrt[2+sqrt(2)] = 1.847759 Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign General of army srit Colonel of regiment srit Externallinks

As abstract polytope rawvatoth is isomorphic to wavitoth, thereby replacing octagons by octagrams, resp. socco by gocco and tic by quith. – As such rawvatoth is a lieutenant.

Incidence matrix according to Dynkin symbol

```o3x3o4/3x4*b

. . .   .    | 96 |   4  2 |  2  2  4  1 |  1 2 2
-------------+----+--------+-------------+-------
. x .   .    |  2 | 192  * |  1  1  1  0 |  1 1 1
. . .   x    |  2 |   * 96 |  0  0  2  1 |  0 1 2
-------------+----+--------+-------------+-------
o3x .   .    |  3 |   3  0 | 64  *  *  * |  1 1 0
. x3o   .    |  3 |   3  0 |  * 64  *  * |  1 0 1
. x .   x4*b |  8 |   4  4 |  *  * 48  * |  0 1 1
. . o4/3x    |  4 |   0  4 |  *  *  * 24 |  0 0 2
-------------+----+--------+-------------+-------
o3x3o   .    ♦  6 |  12  0 |  4  4  0  0 | 16 * *
o3x .   x4*b ♦ 24 |  24 12 |  8  0  6  0 |  * 8 *
. x3o4/3x4*b ♦ 24 |  24 24 |  0  8  6  6 |  * * 8
```

```o3x3/2o4x4*b

. .   . .    | 96 |   4  2 |  2  2  4  1 |  1 2 2
-------------+----+--------+-------------+-------
. x   . .    |  2 | 192  * |  1  1  1  0 |  1 1 1
. .   . x    |  2 |   * 96 |  0  0  2  1 |  0 1 2
-------------+----+--------+-------------+-------
o3x   . .    |  3 |   3  0 | 64  *  *  * |  1 1 0
. x3/2o .    |  3 |   3  0 |  * 64  *  * |  1 0 1
. x   . x4*b |  8 |   4  4 |  *  * 48  * |  0 1 1
. .   o4x    |  4 |   0  4 |  *  *  * 24 |  0 0 2
-------------+----+--------+-------------+-------
o3x3/2o .    ♦  6 |  12  0 |  4  4  0  0 | 16 * *
o3x   . x4*b ♦ 24 |  24 12 |  8  0  6  0 |  * 8 *
. x3/2o4x4*b ♦ 24 |  24 24 |  0  8  6  6 |  * * 8
```

```o3/2x3o4/3x4*b

.   . .   .    | 96 |   4  2 |  2  2  4  1 |  1 2 2
---------------+----+--------+-------------+-------
.   x .   .    |  2 | 192  * |  1  1  1  0 |  1 1 1
.   . .   x    |  2 |   * 96 |  0  0  2  1 |  0 1 2
---------------+----+--------+-------------+-------
o3/2x .   .    |  3 |   3  0 | 64  *  *  * |  1 1 0
.   x3o   .    |  3 |   3  0 |  * 64  *  * |  1 0 1
.   x .   x4*b |  8 |   4  4 |  *  * 48  * |  0 1 1
.   . o4/3x    |  4 |   0  4 |  *  *  * 24 |  0 0 2
---------------+----+--------+-------------+-------
o3/2x3o   .    ♦  6 |  12  0 |  4  4  0  0 | 16 * *
o3/2x .   x4*b ♦ 24 |  24 12 |  8  0  6  0 |  * 8 *
.   x3o4/3x4*b ♦ 24 |  24 24 |  0  8  6  6 |  * * 8
```

```o3/2x3/2o4x4*b

.   .   . .    | 96 |   4  2 |  2  2  4  1 |  1 2 2
---------------+----+--------+-------------+-------
.   x   . .    |  2 | 192  * |  1  1  1  0 |  1 1 1
.   .   . x    |  2 |   * 96 |  0  0  2  1 |  0 1 2
---------------+----+--------+-------------+-------
o3/2x   . .    |  3 |   3  0 | 64  *  *  * |  1 1 0
.   x3/2o .    |  3 |   3  0 |  * 64  *  * |  1 0 1
.   x   . x4*b |  8 |   4  4 |  *  * 48  * |  0 1 1
.   .   o4x    |  4 |   0  4 |  *  *  * 24 |  0 0 2
---------------+----+--------+-------------+-------
o3/2x3/2o .    ♦  6 |  12  0 |  4  4  0  0 | 16 * *
o3/2x   . x4*b ♦ 24 |  24 12 |  8  0  6  0 |  * 8 *
.   x3/2o4x4*b ♦ 24 |  24 24 |  0  8  6  6 |  * * 8
```