This polychoron is just an edge-faceting of tetaco.

Note that this reduction omits the x3/2x fully, while otherwise completely coincident elements become identified.

Incidence matrix according to Dynkin symbol

reduced( ox3/2ox3xx&#x by x3/2x )   → height = sqrt(5/8) = 0.790569
(tet || cho)

         o.3/2o.3o.        | 4  * | 3  3  0  0 | 3  3  6 0 0 | 1 3 3 0
reduced( .o3/2.o3.o      ) | * 12 | 0  1  2  2 | 0  2  2 2 2 | 0 2 2 1
---------------------------+------+------------+-------------+--------
         ..   .. x.        | 2  0 | 6  *  *  * | 2  0  2 0 0 | 1 1 2 0
         oo3/2oo3oo&#x     | 1  1 | * 12  *  * | 0  2  2 0 0 | 0 2 2 0
reduced( .x   .. ..    & ) | 0  2 | *  * 12  * | 0  1  0 1 1 | 0 1 1 1
         ..   .. .x        | 0  2 | *  *  * 12 | 0  0  1 1 1 | 0 1 1 1
---------------------------+------+------------+-------------+--------
         ..   o.3x.        | 3  0 | 3  0  0  0 | 4  *  * * * | 1 0 1 0
reduced( ox   .. ..&#x & ) | 1  2 | 0  2  1  0 | * 12  * * * | 0 1 1 0
         ..   .. xx&#x     | 2  2 | 1  2  0  1 | *  * 12 * * | 0 1 1 0
         .x   .. .x        | 0  4 | 0  0  2  2 | *  *  * 6 * | 0 1 0 1
         ..   .x3.x        | 0  6 | 0  0  3  3 | *  *  * * 4 | 0 0 1 1
---------------------------+------+------------+-------------+--------
         o.3/2o.3x.        ♦ 4  0 | 6  0  0  0 | 4  0  0 0 0 | 1 * * *
         ox   .. xx&#x     ♦ 2  4 | 1  4  2  2 | 0  2  2 1 0 | * 6 * *
         ..   ox3xx&#x     ♦ 3  6 | 3  6  3  3 | 1  3  3 0 1 | * * 4 *
reduced( .x3/2.x3.x      ) ♦ 0 12 | 0  0 12 12 | 0  0  0 6 4 | * * * 1

reduced( xx3/2xx3ox&#x by x3/2x )   → height = sqrt(5/8) = 0.790569
(tet || cho)

reduced( o.3/2o.3o.      ) | 4  * | 3  3  0  0 | 3  6  3 0 0 | 1 3 3 0
reduced( .o3/2.o3.o      ) | * 12 | 0  1  2  2 | 0  2  2 2 2 | 0 2 2 1
---------------------------+------+------------+-------------+--------
reduced( x.   .. ..    & ) | 2  0 | 6  *  *  * | 2  2  0 0 0 | 1 1 2 0
         oo3/2oo3oo&#x     | 1  1 | * 12  *  * | 0  2  2 0 0 | 0 2 2 0
reduced( .x   .. ..    & ) | 0  2 | *  * 12  * | 0  1  0 1 1 | 0 1 1 1
         ..   .. .x        | 0  2 | *  *  * 12 | 0  0  1 1 1 | 0 1 1 1
---------------------------+------+------------+-------------+--------
         ..   x.3o.        | 3  0 | 3  0  0  0 | 4  *  * * * | 1 0 1 0
reduced( xx   .. ..&#x & ) | 2  2 | 1  2  1  0 | * 12  * * * | 0 1 1 0
         ..   .. ox&#x     | 1  2 | 0  2  0  1 | *  * 12 * * | 0 1 1 0
         .x   .. .x        | 0  4 | 0  0  2  2 | *  *  * 6 * | 0 1 0 1
         ..   .x3.x        | 0  6 | 0  0  3  3 | *  *  * * 4 | 0 0 1 1
---------------------------+------+------------+-------------+--------
reduced( x.3/2x.3o.      ) ♦ 4  0 | 6  0  0  0 | 4  0  0 0 0 | 1 * * *
         xx   .. ox&#x     ♦ 2  4 | 1  4  2  2 | 0  2  2 1 0 | * 6 * *
         ..   ox3xx&#x     ♦ 3  6 | 3  6  3  3 | 1  3  3 0 1 | * * 4 *
reduced( .x3/2.x3.x      ) ♦ 0 12 | 0  0 12 12 | 0  0  0 6 4 | * * * 1