Acronym ... Name 2tho+24{4} (?) Circumradius 1/sqrt(2) = 0.707107 Coordinates in orthoplex position:   (1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign in hemitesseract position:   (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all even permutations, all even changes of sign in "the other" (mirrored) hemitesseract position:   (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), -1/sqrt(8))   & all even permutations, all even changes of sign General of army hex Colonel of regiment hex Confer non-Grünbaumian master: tho

This Grünbaumian polychoron can be obtained constructively by adjoining 2 mutually inverted copies of 2thah, joined at their squares, and putting tet at all 8 triangles each, pointing all into the same 4th direction. The other 8 tet, adjoined to the 2nd 2thah, point into the opposite direction (thus becoming point-inverive too). The remaining 2thah finally are interlinked to the open tetrahedral faces.

Incidence matrix according to Dynkin symbol

```x3o3/2x *b3o

. .   .    . | 32 |  3  3 |  3  3  3 | 3 1 1
-------------+----+-------+----------+------
x .   .    . |  2 | 48  * |  2  1  0 | 2 1 0
. .   x    . |  2 |  * 48 |  0  1  2 | 2 0 1
-------------+----+-------+----------+------
x3o   .    . |  3 |  3  0 | 32  *  * | 1 1 0
x .   x    . |  4 |  2  2 |  * 24  * | 2 0 0
. o3/2x    . |  3 |  0  3 |  *  * 32 | 1 0 1
-------------+----+-------+----------+------
x3o3/2x    . ♦ 12 | 12 12 |  4  6  4 | 8 * *
x3o   . *b3o ♦  4 |  6  0 |  4  0  0 | * 8 *
. o3/2x *b3o ♦  4 |  0  6 |  0  0  4 | * * 8
```

```x3o3/2x *b3/2o

. .   .      . | 32 |  3  3 |  3  3  3 | 3 1 1
---------------+----+-------+----------+------
x .   .      . |  2 | 48  * |  2  1  0 | 2 1 0
. .   x      . |  2 |  * 48 |  0  1  2 | 2 0 1
---------------+----+-------+----------+------
x3o   .      . |  3 |  3  0 | 32  *  * | 1 1 0
x .   x      . |  4 |  2  2 |  * 24  * | 2 0 0
. o3/2x      . |  3 |  0  3 |  *  * 32 | 1 0 1
---------------+----+-------+----------+------
x3o3/2x      . ♦ 12 | 12 12 |  4  6  4 | 8 * *
x3o   . *b3/2o ♦  4 |  6  0 |  4  0  0 | * 8 *
. o3/2x *b3/2o ♦  4 |  0  6 |  0  0  4 | * * 8
```