This polychoron is just an edge-faceting of coatut.

It shall be pointed out that in the here being used reduction the x3/2x faces of the base 2tut cancel completely out, while their coincident pairs of hexagons will get identified instead.

Incidence matrix according to Dynkin symbol

reduced( xx3/2xo3xx3*a&#x by x.3/2x.3x.3*a )   → hight = sqrt(5/8) = 0.790569

         o.3/2o.3o.3*a        | 12  * |  2 1  2  0  0 | 2  2  2  2 0 0 0 | 1 2 2 0
         .o3/2.o3.o3*a        |  * 12 |  0 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
reduced( ..   .. x.         ) |  2  0 |  * 6  *  *  * | 2  0  0  2 0 0 0 | 0 2 2 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.   .. x.3*a    & ) |  6  0 |  3 3  0  0  0 | 4  *  *  * * * * | 0 1 1 0
         xx   .. ..   &#x     |  2  2 |  1 0  2  1  0 | * 12  *  * * * * | 1 1 0 0
         ..   xo ..   &#x     |  2  1 |  1 0  2  0  0 | *  * 12  * * * * | 1 0 1 0
         ..   .. xx   &#x     |  2  2 |  0 1  2  0  1 | *  *  * 12 * * * | 0 1 1 0
         .x3/2.o ..           |  0  3 |  0 0  0  3  0 | *  *  *  * 4 * * | 1 0 0 1
         .x   .. .x3*a        |  0  6 |  0 0  0  3  3 | *  *  *  * * 4 * | 0 1 0 1
         ..   .o3.x           |  0  3 |  0 0  0  0  3 | *  *  *  * * * 4 | 0 0 1 1
------------------------------+-------+---------------+------------------+--------
reduced( xx3/2xo ..   &#x   ) ♦  3  3 |  3 0  6  3  0 | 0  3  3  0 1 0 0 | 4 * * *
         xx   .. xx3*a&#x     ♦  6  6 |  3 3  6  3  3 | 1  3  0  3 0 1 0 | * 4 * *
         ..   xo3xx   &#x     ♦  6  3 |  3 3  6  0  3 | 1  0  3  3 0 0 1 | * * 4 *
         .x3/2.o3.x           ♦  0 12 |  0 0  0 12 12 | 0  0  0  0 4 4 4 | * * * 1