Acronym ... Name 2titho (?) Circumradius sqrt(5/2) = 1.581139 Coordinates (sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign General of army thex Colonel of regiment thex Confer non-Grünbaumian master: titho

This Grünbaumian polychoron indeed has all elements in coincident pairs, only the Grünbaumian double-covers of thah interconnect the 2 layers. Esp. the toes come in 4 coincident pairs, while the 2 types of tuts coincide one by one of either type each. Each individual vertex figure is the same as the vertex figure of titho: a tall pyramid based on a crossed square.

Incidence matrix according to Dynkin symbol

```x3x3x3o3/2*a

. . . .      | 96 |  2  1  2 |  2  2  1  2  1 | 2 1 1 1
-------------+----+----------+----------------+--------
x . . .      |  2 | 96  *  * |  1  1  1  0  0 | 1 1 1 0
. x . .      |  2 |  * 48  * |  2  0  0  2  0 | 2 1 0 1
. . x .      |  2 |  *  * 96 |  0  1  0  1  1 | 1 0 1 1
-------------+----+----------+----------------+--------
x3x . .      |  6 |  3  3  0 | 32  *  *  *  * | 1 1 0 0
x . x .      |  4 |  2  0  2 |  * 48  *  *  * | 1 0 1 0
x . . o3/2*a |  3 |  3  0  0 |  *  * 32  *  * | 0 1 1 0
. x3x .      |  6 |  0  3  3 |  *  *  * 32  * | 1 0 0 1
. . x3o      |  3 |  0  0  3 |  *  *  *  * 32 | 0 0 1 1
-------------+----+----------+----------------+--------
x3x3x .      ♦ 24 | 12 12 12 |  4  6  0  4  0 | 8 * * *
x3x . o3/2*a ♦ 12 | 12  6  0 |  4  0  4  0  0 | * 8 * *
x . x3o3/2*a ♦ 12 | 12  0 12 |  0  6  4  0  4 | * * 8 *
. x3x3o      ♦ 12 |  0  6 12 |  0  0  0  4  4 | * * * 8
```