Acronym thatoth
Cross sections
` ©`
Circumradius sqrt[(5+sqrt(2))/2] = 1.790840
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, (sqrt(2)-1)/2)   & all permutations, all changes of sign
Colonel of regiment (is itself locally convex – uniform polychoral members:
 by cells: cotco tic tut thatoth 8 8 16
)
External

As abstract polytope thatoth is isomorphic to thaquitoth, thereby interchanging the roles of octagrams and octagons, resp. replacing tic by quith.

Incidence matrix according to Dynkin symbol

```o3x3x4/3x4*b

. . .   .    | 192 |   2  1  1 |  1  2  2  1 |  1 1 2
-------------+-----+-----------+-------------+-------
. x .   .    |   2 | 192  *  * |  1  1  1  0 |  1 1 1
. . x   .    |   2 |   * 96  * |  0  2  0  1 |  1 0 2
. . .   x    |   2 |   *  * 96 |  0  0  2  1 |  0 1 2
-------------+-----+-----------+-------------+-------
o3x .   .    |   3 |   3  0  0 | 64  *  *  * |  1 1 0
. x3x   .    |   6 |   3  3  0 |  * 64  *  * |  1 0 1
. x .   x4*b |   8 |   4  0  4 |  *  * 48  * |  0 1 1
. . x4/3x    |   8 |   0  4  4 |  *  *  * 24 |  0 0 2
-------------+-----+-----------+-------------+-------
o3x3x   .    ♦  12 |  12  6  0 |  4  4  0  0 | 16 * *
o3x .   x4*b ♦  24 |  24  0 12 |  8  0  6  0 |  * 8 *
. x3x4/3x4*b ♦  48 |  24 24 24 |  0  8  6  6 |  * * 8
```

```o3/2x3x4/3x4*b

.   . .   .    | 192 |   2  1  1 |  1  2  2  1 |  1 1 2
---------------+-----+-----------+-------------+-------
.   x .   .    |   2 | 192  *  * |  1  1  1  0 |  1 1 1
.   . x   .    |   2 |   * 96  * |  0  2  0  1 |  1 0 2
.   . .   x    |   2 |   *  * 96 |  0  0  2  1 |  0 1 2
---------------+-----+-----------+-------------+-------
o3/2x .   .    |   3 |   3  0  0 | 64  *  *  * |  1 1 0
.   x3x   .    |   6 |   3  3  0 |  * 64  *  * |  1 0 1
.   x .   x4*b |   8 |   4  0  4 |  *  * 48  * |  0 1 1
.   . x4/3x    |   8 |   0  4  4 |  *  *  * 24 |  0 0 2
---------------+-----+-----------+-------------+-------
o3/2x3x   .    ♦  12 |  12  6  0 |  4  4  0  0 | 16 * *
o3/2x .   x4*b ♦  24 |  24  0 12 |  8  0  6  0 |  * 8 *
.   x3x4/3x4*b ♦  48 |  24 24 24 |  0  8  6  6 |  * * 8
```

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