This polychoron is just an edge-faceting of rap.

Incidence matrix according to Dynkin symbol

reduced( ox3/2xx3oo&#x by x3/2x )   → height = sqrt(5/8) = 0.790569

         o.3/2o.3o.        | 6 * |  4  2 0 | 2 2 1  4 0 | 1 2 2 0
reduced( .o3/2.o3.o      ) | * 4 |  0  3 3 | 0 0 3  6 3 | 0 3 3 1
---------------------------+-----+---------+------------+--------
         ..   x. ..        | 2 0 | 12  * * | 1 1 0  1 0 | 1 1 1 0
         oo3/2oo3oo&#x     | 1 1 |  * 12 * | 0 0 1  2 0 | 0 2 1 0
reduced( .x   .. ..    & ) | 0 2 |  *  * 6 | 0 0 1  2 2 | 0 2 2 1
---------------------------+-----+---------+------------+--------
         o.3/2x. ..        | 3 0 |  3  0 0 | 4 * *  * * | 1 1 0 0
         ..   x.3o.        | 3 0 |  3  0 0 | * 4 *  * * | 1 0 1 0
         ox   .. ..&#x     | 1 2 |  0  2 1 | * * 6  * * | 0 2 0 0
         ..   xx ..&#x     | 2 2 |  1  2 1 | * * * 12 * | 0 1 1 0
         ..   .x3.o        | 0 3 |  0  0 3 | * * *  * 4 | 0 0 1 1
---------------------------+-----+---------+------------+--------
         o.3/2x.3o.        ♦ 6 0 | 12  0 0 | 4 4 0  0 0 | 1 * * *
reduced( ox3/2xx ..&#x   ) ♦ 3 3 |  3  6 3 | 1 0 3  3 0 | * 4 * *
         ..   xx3oo&#x     ♦ 3 3 |  3  3 3 | 0 1 0  3 1 | * * 4 *
reduced( .x3/2.x3.x      ) ♦ 0 4 |  0  0 6 | 0 0 0  0 4 | * * * 1