Acronym ... Name 2tho (?) 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   Grünbaumian relatives: 2tho+24{4}

This Grünbaumian polychoron indeed has all elements in coincident pairs, only the vertices are identified; thus the vertex figure becomes a Grünbaumian double-cover of thah.

Incidence matrix according to Dynkin symbol

```x3o3o3o3/2*a

. . . .      | 8 ♦ 12 | 12 12 | 4 6 4
-------------+---+----+-------+------
x . . .      | 2 | 48 |  2  2 | 1 2 1
-------------+---+----+-------+------
x3o . .      | 3 |  3 | 32  * | 1 1 0
x . . o3/2*a | 3 |  3 |  * 32 | 0 1 1
-------------+---+----+-------+------
x3o3o .      ♦ 4 |  6 |  4  0 | 8 * *
x3o . o3/2*a ♦ 6 | 12 |  4  4 | * 8 *
x . o3o3/2*a ♦ 4 |  6 |  0  4 | * * 8
```

```x3o3o3/2o3*a

. . .   .    | 8 ♦ 12 | 12 12 | 4 6 4
-------------+---+----+-------+------
x . .   .    | 2 | 48 |  2  2 | 1 2 1
-------------+---+----+-------+------
x3o .   .    | 3 |  3 | 32  * | 1 1 0
x . .   o3*a | 3 |  3 |  * 32 | 0 1 1
-------------+---+----+-------+------
x3o3o   .    ♦ 4 |  6 |  4  0 | 8 * *
x3o .   o3*a ♦ 6 | 12 |  4  4 | * 8 *
x . o3/2o3*a ♦ 4 |  6 |  0  4 | * * 8
```

```x3o3/2o3/2o3/2*a

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

```x3/2o3o3/2o3/2*a

.   . .   .      | 8 ♦ 12 | 12 12 | 4 6 4
-----------------+---+----+-------+------
x   . .   .      | 2 | 48 |  2  2 | 1 2 1
-----------------+---+----+-------+------
x3/2o .   .      | 3 |  3 | 32  * | 1 1 0
x   . .   o3/2*a | 3 |  3 |  * 32 | 0 1 1
-----------------+---+----+-------+------
x3/2o3o   .      ♦ 4 |  6 |  4  0 | 8 * *
x3/2o .   o3/2*a ♦ 6 | 12 |  4  4 | * 8 *
x   . o3/2o3/2*a ♦ 4 |  6 |  0  4 | * * 8
```

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