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         o3o         
                     
      q3o   o3q      
                     
   o3q         q3o   
                     
o3o   q3o   o3q   o3o

This polyteron is obtained as a diminishing of ico, in fact by cyclically chopping off 3 cubpies.

Incidence matrix according to Dynkin symbol

((sxo3sox oqo3ooq))&#zx   → all heights = 0
(tegum sum of h-{3} and 2 bidual (x,q)-triddips)

hemi( o..3o.. ) o..3o..       | 3 * * | 3 3 0  0  0 0 |  6 3 3 0  0  0 0 | 3 3 2 0
      .o.3.o.   .o.3.o.       | * 9 * | 1 0 2  2  2 0 |  2 2 1 1  4  2 0 | 2 2 1 2
      ..o3..o   ..o3..o       | * * 9 | 0 1 0  2  2 2 |  2 1 2 0  2  4 1 | 2 2 1 2
------------------------------+-------+---------------+------------------+--------
      oo.3oo.   oo.3oo.  &#x  | 1 1 0 | 9 * *  *  * * |  2 2 0 0  0  0 0 | 1 2 1 0
      o.o3o.o   o.o3o.o  &#x  | 1 0 1 | * 9 *  *  * * |  2 0 2 0  0  0 0 | 2 1 1 0
      .x. ...   ... ...       | 0 2 0 | * * 9  *  * * |  0 0 0 1  2  0 0 | 1 0 0 2
      .oo3.oo   .oo3.oo  &#x  | 0 1 1 | * * * 18  * * |  1 0 0 0  1  1 0 | 1 1 0 1  underneath remaining
      .oo3.oo   .oo3.oo  &#x  | 0 1 1 | * * *  * 18 * |  0 1 1 0  1  1 0 | 1 1 1 1  underneath omitted
      ... ..x   ... ...       | 0 0 2 | * * *  *  * 9 |  0 0 0 0  0  2 1 | 0 1 0 2
------------------------------+-------+---------------+------------------+--------
      ooo3ooo   ooo3ooo  &#x  | 1 1 1 | 1 1 0  1  0 0 | 18 * * *  *  * * | 1 1 0 0
      ... ...   oqo ...  &#xt | 1 2 1 | 2 0 0  0  2 0 |  * 9 * *  *  * * | 0 1 1 0  stack: A-B-C
      ... ...   ... ooq  &#xt | 1 1 2 | 0 2 0  0  2 0 |  * * 9 *  *  * * | 1 0 1 0  stack: A-C-B
      .x.3.o.   ... ...       | 0 3 0 | 0 0 3  0  0 0 |  * * * 3  *  * * | 0 0 0 2
      .xo ...   ... ...  &#x  | 0 2 1 | 0 0 1  1  1 0 |  * * * * 18  * * | 1 0 0 1
      ... .ox   ... ...  &#x  | 0 1 2 | 0 0 0  1  1 1 |  * * * *  * 18 * | 0 1 0 1
      ..o3..x   ... ...       | 0 0 3 | 0 0 0  0  0 3 |  * * * *  *  * 3 | 0 0 0 2
------------------------------+-------+---------------+------------------+--------
    ((sxo ...   ... ooq))&#zx ♦ 1 2 2 | 1 2 1  2  2 0 |  2 0 1 0  2  0 0 | 9 * * *
    ((... sox   oqo ...))&#zx ♦ 1 2 2 | 2 1 0  2  2 1 |  2 1 0 0  0  2 0 | * 9 * *
      ... ...   oqo3ooq  &#xt ♦ 2 3 3 | 3 3 0  0  6 0 |  0 3 3 0  0  0 0 | * * 3 *  stack: A-B-C-A
      .xo3.ox   ... ...  &#x  ♦ 0 3 3 | 0 0 3  3  3 3 |  0 0 0 1  3  3 1 | * * * 6