This polychoron is just an edge-faceting of octaco.

It shall be pointed out that in the here being used reduction the x3/2x faces of the top-base 2oct cancel completely out, while their coincident pairs of triangles will get identified instead. (Therefore one might be tempted to name it rather a hollow thah atop oho instead, but then its diametral squares would have to vanish somehow mystically.)

Incidence matrix according to Dynkin symbol

reduced( xx3/2xo3ox3*a&#x by x.3/2x.3o.3*a )   → height = 1/sqrt(2) = 0.707107
(pseudo 2oct || oho)

         o.3/2o.3o.3*a        | 6  * |  4  4  0  0 | 2  4  4  2 0 0 0 | 2 2 2 0
         .o3/2.o3.o3*a        | * 12 |  0  2  2  2 | 0  2  1  2 1 2 1 | 1 2 1 1
------------------------------+------+-------------+------------------+--------
reduced( x.   .. ..       & ) | 2  0 | 12  *  *  * | 1  1  1  0 0 0 0 | 1 1 1 0
         oo3/2oo3oo3*a&#x     | 1  1 |  * 24  *  * | 0  1  1  1 0 0 0 | 1 1 1 0
         .x   .. ..           | 0  2 |  *  * 12  * | 0  1  0  0 1 1 0 | 1 1 0 1
         ..   .. .x           | 0  2 |  *  *  * 12 | 0  0  0  1 0 1 1 | 0 1 1 1
------------------------------+------+-------------+------------------+--------
reduced( x.   .. o.3*a    & ) | 3  0 |  3  0  0  0 | 4  *  *  * * * * | 0 1 1 0
         xx   .. ..   &#x     | 2  2 |  1  2  1  0 | * 12  *  * * * * | 1 1 0 0
         ..   xo ..   &#x     | 2  1 |  1  2  0  0 | *  * 12  * * * * | 1 0 1 0
         ..   .. ox   &#x     | 1  2 |  0  2  0  1 | *  *  * 12 * * * | 0 1 1 0
         .x3/2.o ..           | 0  3 |  0  0  3  0 | *  *  *  * 4 * * | 1 0 0 1
         .x   .. .x3*a        | 0  6 |  0  0  3  3 | *  *  *  * * 4 * | 0 1 0 1
         ..   .o3.x           | 0  3 |  0  0  0  3 | *  *  *  * * * 4 | 0 0 1 1
------------------------------+------+-------------+------------------+--------
reduced( xx3/2xo ..   &#x   ) ♦ 3  3 |  3  6  3  0 | 0  3  3  0 1 0 0 | 4 * * *
         xx   .. ox3*a&#x     ♦ 3  6 |  3  6  3  3 | 1  3  0  3 0 1 0 | * 4 * *
         ..   xo3ox   &#x     ♦ 3  3 |  3  6  0  3 | 1  0  3  3 0 0 1 | * * 4 *
         .x3/2.o3.x           ♦ 0 12 |  0  0 12 12 | 0  0  0  0 4 4 4 | * * * 1