©
its 3 tricu rings:


 ©
its cubes:
 ©

         x3x         
           A         
                     
      u3x   x3u      
        B     B          with:
                         H=3x=x+u
   x3u  oH3Ho  u3x   
     B     C     B   
                     
x3x   u3x   x3u   x3x
  A     B     B     A

Incidence matrix

18  * * |  2  2  0  0  0  0 | 1  2  2  1  0  0 | 2  2 0  (A) toe-toe connection vertices
 * 36 * |  0  1  1  1  1  1 | 0  2  1  1  3  1 | 1  3 1  (B) non-connecting toe vertices
 *  * 6 |  0  0  0  0  0  6 | 0  0  0  0  6  3 | 0  3 2  (C) cube-cube vertices (still with rico verfs)
--------+-------------------+------------------+-------
 2  0 0 | 18  *  *  *  *  * | 1  1  1  0  0  0 | 2  1 0  (a) toe-toe-connecting edges
 1  1 0 |  * 36  *  *  *  * | 0  1  1  1  0  0 | 1  2 0  (b) non-parallel toe-square-edges
 0  2 0 |  *  * 18  *  *  * | 0  1  1  0  0  1 | 1  2 0  (c) parallel toe edges
 0  2 0 |  *  *  * 18  *  * | 0  2  0  0  2  0 | 1  2 1  (d) toe-cube edges
 0  2 0 |  *  *  *  * 18  * | 0  0  0  1  2  0 | 0  2 1  (e) remaining equatorial zickzack cube edges
 0  1 1 |  *  *  *  *  * 36 | 0  0  0  0  2  1 | 0  2 1  (c) polar cube edges
--------+-------------------+------------------+-------
 6  0 0 |  6  0  0  0  0  0 | 3  *  *  *  *  * | 2  0 0  toe-toe connection {6}
 2  4 0 |  1  2  1  2  0  0 | * 18  *  *  *  * | 1  1 0  remaining toe-{6}
 2  2 0 |  1  2  1  0  0  0 | *  * 18  *  *  * | 1  1 0  toe-{4}
 1  2 0 |  0  2  0  0  1  0 | *  *  * 18  *  * | 0  2 0
 0  3 1 |  0  0  0  1  1  2 | *  *  *  * 36  * | 0  1 1  cube-{4}
 0  2 1 |  0  0  1  0  0  2 | *  *  *  *  * 18 | 0  2 0
--------+-------------------+------------------+-------
12 12 0 | 12 12  6  6  0  0 | 2  6  6  0  0  0 | 3  * *  toe
 2  6 1 |  1  4  2  2  2  4 | 0  1  1  2  2  2 | * 18 *  tricu *)
 0  6 2 |  0  0  0  3  3  6 | 0  0  0  0  6  0 | *  * 6  cube

*)   A--a--A
    /b     b\
   b_B--c--B_b
  Be  f   f  eB
   \   \ /   /
    d  _C_  d
     Bf-c-fB