This polychoron is just an edge-faceting of rap.

The mere reduction of the underlying Grünbaumian lace prism of the first case would be degenerate as octs and thahs not only become corealmic, they even share their respective edge sets completely. However, when blending those facets, each pair would result in an inverted oriented thah instead. Thereby the bottom base finally gets reduced to the 3 diametral squares of an oct (as being used within the thah) only.

The second and third cases work out like that by mere reduction, i.e. without resorting to any further blending. However the top base of the second case in the underlying Grünbaumian lace prism is a regular tet, whereas in the other cases it is the itself Grünbaumian 3tet instead.

Incidence matrix according to Dynkin symbol

reduced( xx3/2xo3ox&#x by x3/2x )   → height = sqrt(5/8) = 0.790569
(tet || "squares of thah")

reduced( o.3/2o.3o.                    ) | 4 * | 3  3  0 | 3  6  3 0 | 1 3 3
reduced( .o3/2.o3.o                    ) | * 6 | 0  2  4 | 0  4  4 2 | 0 2 4
-----------------------------------------+-----+---------+-----------+------
reduced( x.   .. ..    & ..   x. ..    ) | 2 0 | 6  *  * | 2  2  0 0 | 1 2 1
         oo3/2oo3oo&#x                   | 1 1 | * 12  * | 0  2  2 0 | 0 2 2
reduced( .x   .. ..    & ..   .. .x    ) | 0 2 | *  * 12 | 0  1  1 1 | 0 1 2
-----------------------------------------+-----+---------+-----------+------
         ..   x.3o.                      | 3 0 | 3  0  0 | 4  *  * * | 1 1 0
         xx   .. ..&#x                   | 2 2 | 1  2  1 | * 12  * * | 0 1 1
         ..   .. ox&#x                   | 1 2 | 0  2  1 | *  * 12 * | 0 1 1
         .x   .. .x                      | 0 4 | 0  0  4 | *  *  * 3 | 0 0 2
-----------------------------------------+-----+---------+-----------+------
reduced( x.3/2x.3o.                    ) ♦ 4 0 | 6  0  0 | 4  0  0 0 | 1 * 
blended( xx3/2xo ..&#x & ..   xo3ox&#x ) ♦ 3 3 | 3  6  3 | 1  3  3 0 | * 4 *
         xx   .. ox&#x                   ♦ 2 4 | 1  4  4 | 0  2  2 1 | * * 6

reduced( xx3/2ox3/2ox&#x by x3/2x )   → height = sqrt(5/8) = 0.790569
(tet || "squares of thah")

         o.3/2o.3/2o.        | 4 * | 3  3  0 | 3  6  3 0 | 1 3 3
reduced( .o3/2.o3/2.o      ) | * 6 | 0  2  4 | 0  4  4 2 | 0 2 4
-----------------------------+-----+---------+-----------+------
         x.   ..   ..        | 2 0 | 6  *  * | 2  2  0 0 | 1 2 1
         oo3/2oo3/2oo&#x     | 1 1 | * 12  * | 0  2  2 0 | 0 2 2
reduced( .x   ..   ..    & ) | 0 2 | *  * 12 | 0  1  1 1 | 0 1 2
-----------------------------+-----+---------+-----------+------
         x.3/2o.   ..        | 3 0 | 3  0  0 | 4  *  * * | 1 1 0
         xx   ..   ..&#x     | 2 2 | 1  2  1 | * 12  * * | 0 1 1
reduced( ..   ox   ..&#x & ) | 1 2 | 0  2  1 | *  * 12 * | 0 1 1
reduced( .x   ..   .x      ) | 0 4 | 0  0  4 | *  *  * 3 | 0 0 2
-----------------------------+-----+---------+-----------+------
         x.3/2o.3/2o.        ♦ 4 0 | 6  0  0 | 4  0  0 0 | 1 * *
reduced( xx3/2ox   ..&#x   ) ♦ 3 3 | 3  6  3 | 1  3  3 0 | * 4 *
         xx   ..   ox&#x     ♦ 2 4 | 1  4  4 | 0  2  2 1 | * * 6

reduced( xx3/2xx3/2ox&#x by x3/2x )   → height = sqrt(5/8) = 0.790569
(tet || "squares of thah")

         o.3/2o.3/2o.        | 4 * | 3  3  0 | 3  6  3 0 | 1 3 3
reduced( .o3/2.o3/2.o      ) | * 6 | 0  2  4 | 0  4  4 2 | 0 4 2
-----------------------------+-----+---------+-----------+------
reduced( x.   ..   ..    & ) | 2 0 | 6  *  * | 2  2  0 0 | 1 1 2
         oo3/2oo3/2oo&#x     | 1 1 | * 12  * | 0  2  2 0 | 0 2 2
reduced( .x   ..   ..    & ) | 0 2 | *  * 12 | 0  1  1 1 | 0 2 1
-----------------------------+-----+---------+-----------+------
         ..   x.3/2o.        | 3 0 | 3  0  0 | 4  *  * * | 1 0 1
reduced( xx   ..   ..&#x & ) | 2 2 | 1  2  1 | * 12  * * | 0 1 1
         ..   ..   ox&#x     | 1 2 | 0  2  1 | *  * 12 * | 0 1 1
reduced( .x   ..   .x      ) | 0 4 | 0  0  4 | *  *  * 3 | 0 2 0
-----------------------------+-----+---------+-----------+------
reduced( x.3/2x.3/2o.      ) ♦ 4 0 | 6  0  0 | 4  0  0 0 | 1 * *
         xx   ..   ox&#x     ♦ 2 4 | 1  4  4 | 0  2  2 1 | * 6 *
reduced( ..   xx3/2ox&#x   ) ♦ 3 3 | 3  6  3 | 1  3  3 0 | * * 4