This polychoron is just an edge-faceting of rap.

Incidence matrix according to Dynkin symbol

reduced( xx3/2ox3oo3*a&#x by x3/2x ) - height =   → height = sqrt(5/8) = 0.790569
(pseudo tet || pseudo oct)

         o.3/2o.3o.3*a        | 4 * | 3  3  0 | 3  6  3 0 | 3 3 1
reduced( .o3/2.o3.o3*a      ) | * 6 | 0  2  4 | 0  4  4 2 | 2 2 2
------------------------------+-----+---------+-----------+------
reduced( x.   .. ..       & ) | 2 0 | 6  *  * | 2  2  0 0 | 2 2 0
         oo3/2oo3oo3*a&#x     | 1 1 | * 12  * | 0  2  2 0 | 2 1 1
reduced( .x   .. ..       & ) | 0 2 | *  * 12 | 0  1  1 1 | 1 1 1
------------------------------+-----+---------+-----------+------
reduced( x.3/2o. ..       & ) | 3 0 | 3  0  0 | 4  *  * * | 1 1 0
         xx   .. ..   &#x     | 2 2 | 1  2  1 | * 12  * * | 1 1 0
         ..   ox ..   &#x     | 1 2 | 0  2  1 | *  * 12 * | 1 0 1
reduced( .x   .. .o3*a    & ) | 0 3 | 0  0  3 | *  *  * 4 | 0 1 1
------------------------------+-----+---------+-----------+------
reduced( xx3/2ox ..   &#x   ) ♦ 3 3 | 3  6  3 | 1  3  3 0 | 4 * *
         xx   .. oo3*a&#x     ♦ 3 3 | 3  3  3 | 1  3  0 1 | * 4 *
         ..   ox3oo   &#x     ♦ 1 3 | 0  3  3 | 0  0  3 1 | * * 4

reduced( xx3/2ox3/2oo3/2*a&#x by x3/2x ) - height =   → height = sqrt(5/8) = 0.790569
(pseudo tet || pseudo oct)

         o.3/2o.3/2o.3/2*a        | 4 * | 3  3  0 | 3  6  3 0 | 3 3 1
reduced( .o3/2.o3/2.o3/2*a      ) | * 6 | 0  2  4 | 0  4  4 2 | 2 2 2
----------------------------------+-----+---------+-----------+------
reduced( x.   ..   ..         & ) | 2 0 | 6  *  * | 2  2  0 0 | 2 2 0
         oo3/2oo3/2oo3/2*a&#x     | 1 1 | * 12  * | 0  2  2 0 | 2 1 1
reduced( .x   ..   ..         & ) | 0 2 | *  * 12 | 0  1  1 1 | 1 1 1
----------------------------------+-----+---------+-----------+------
reduced( x.3/2o.   ..         & ) | 3 0 | 3  0  0 | 4  *  * * | 1 1 0
         xx   ..   ..     &#x     | 2 2 | 1  2  1 | * 12  * * | 1 1 0
         ..   ox   ..     &#x     | 1 2 | 0  2  1 | *  * 12 * | 1 0 1
reduced( .x   ..   .o3/2*a    & ) | 0 3 | 0  0  3 | *  *  * 4 | 0 1 1
----------------------------------+-----+---------+-----------+------
reduced( xx3/2ox   ..     &#x   ) ♦ 3 3 | 3  6  3 | 1  3  3 0 | 4 * *
         xx   ..   oo3/2*a&#x     ♦ 3 3 | 3  3  3 | 1  3  0 1 | * 4 *
         ..   ox3/2oo     &#x     ♦ 1 3 | 0  3  3 | 0  0  3 1 | * * 4