2ratho

Acronym	...
Name	2ratho (?)
Circumradius	1
Coordinates	(1, 0, 0, 0) & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign (vertex inscribed tes) or just (1/sqrt(2), 1/sqrt(2), 0, 0) & all permutations, all changes of sign (in dual ico positioning)
General of army	ico
Colonel of regiment	ico
Confer	non-Grünbaumian master: ratho general polytopal classes: Wythoffian polychora

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

Incidence matrix according to Dynkin symbol

x3o3x3o3/2*a

. . . .      | 48 |  4  4 |  2  4  2  2  2 | 2 1 2 1
-------------+----+-------+----------------+--------
x . . .      |  2 | 96  * |  1  1  1  0  0 | 1 1 1 0
. . x .      |  2 |  * 96 |  0  1  0  1  1 | 1 0 1 1
-------------+----+-------+----------------+--------
x3o . .      |  3 |  3  0 | 32  *  *  *  * | 1 1 0 0
x . x .      |  4 |  2  2 |  * 48  *  *  * | 1 0 1 0
x . . o3/2*a |  3 |  3  0 |  *  * 32  *  * | 0 1 1 0
. o3x .      |  3 |  0  3 |  *  *  * 32  * | 1 0 0 1
. . x3o      |  3 |  0  3 |  *  *  *  * 32 | 0 0 1 1
-------------+----+-------+----------------+--------
x3o3x .      ♦ 12 | 12 12 |  4  6  0  4  0 | 8 * * *
x3o . o3/2*a ♦  6 | 12  0 |  4  0  4  0  0 | * 8 * *
x . x3o3/2*a ♦ 12 | 12 12 |  0  6  4  0  4 | * * 8 *
. o3x3o      ♦  6 |  0 12 |  0  0  0  4  4 | * * * 8

x3o3/2x3/2o3/2*a

. .   .   .      | 48 |  4  4 |  2  4  2  2  2 | 2 1 2 1
-----------------+----+-------+----------------+--------
x .   .   .      |  2 | 96  * |  1  1  1  0  0 | 1 1 1 0
. .   x   .      |  2 |  * 96 |  0  1  0  1  1 | 1 0 1 1
-----------------+----+-------+----------------+--------
x3o   .   .      |  3 |  3  0 | 32  *  *  *  * | 1 1 0 0
x .   x   .      |  4 |  2  2 |  * 48  *  *  * | 1 0 1 0
x .   .   o3/2*a |  3 |  3  0 |  *  * 32  *  * | 0 1 1 0
. o3/2x   .      |  3 |  0  3 |  *  *  * 32  * | 1 0 0 1
. .   x3/2o      |  3 |  0  3 |  *  *  *  * 32 | 0 0 1 1
-----------------+----+-------+----------------+--------
x3o3/2x   .      ♦ 12 | 12 12 |  4  6  0  4  0 | 8 * * *
x3o   .   o3/2*a ♦  6 | 12  0 |  4  0  4  0  0 | * 8 * *
x .   x3/2o3/2*a ♦ 12 | 12 12 |  0  6  4  0  4 | * * 8 *
. o3/2x3/2o      ♦  6 |  0 12 |  0  0  0  4  4 | * * * 8

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