Acronym ...
Name quith atop "squares of thah",
reduced quith atop 2oct+6{4}
Circumradius sqrt[(1+2 sqrt(2))/7] = 0.739539
Face vector 30, 96, 89, 27
Confer
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

reduced( xo4/3xx3/2ox&#x by oct )   → height = sqrt[2 sqrt(2)-1]/2 = 0.676097
(quith || "squares of thah")

         o.4/3o.3/2o.      | 24 * |  1  2  2  0 | 2 1  2  2  1 0 | 1 2  1 1
identif( .o4/3.o3/2.o    ) |  * 6 |  0  0  8  4 | 0 0  4  8  8 2 | 0 4  4 4
---------------------------+------+-------------+----------------+---------
         x.   ..   ..      |  2 0 | 12  *  *  * | 2 0  2  0  0 0 | 1 2  1 0
         ..   x.   ..      |  2 0 |  * 24  *  * | 1 1  0  1  0 0 | 1 1  0 1
         oo4/3oo3/2oo&#x   |  1 1 |  *  * 48  * | 0 0  1  1  1 0 | 0 1  1 1
identif( ..   .x   ..    ) |  0 2 |  *  *  * 12 | 0 0  0  2  2 1 | 0 2  1 2
---------------------------+------+-------------+----------------+---------
         x.4/3x.   ..      |  8 0 |  4  4  0  0 | 6 *  *  *  * * | 1 1  0 0
         ..   x.3/2o.      |  3 0 |  0  3  0  0 | * 8  *  *  * * | 1 0  0 1
         xo   ..   ..&#x   |  2 1 |  1  0  2  0 | * * 24  *  * * | 0 1  1 0
         ..   xx   ..&#x   |  2 2 |  0  1  2  1 | * *  * 24  * * | 0 1  0 1
         ..   ..   ox&#x   |  1 2 |  0  0  2  1 | * *  *  * 24 * | 0 0  1 1
identif( .o4/3.x   ..    ) |  0 4 |  0  0  0  4 | * *  *  *  * 3 | 0 2  0 0
---------------------------+------+-------------+----------------+---------
         x.4/3x.3/2o.       24 0 | 12 24  0  0 | 6 8  0  0  0 0 | 1 *  * *
         xo4/3xx   ..&#x     8 4 |  4  4  8  4 | 1 0  4  4  0 1 | * 6  * *
         xo   ..   ox&#x     2 2 |  1  0  4  1 | 0 0  2  0  2 0 | * * 12 *
reduced( ..   xx3/2ox&#x )   3 3 |  0  3  6  3 | 0 1  0  3  3 0 | * *  * 8

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