©

            o3o            
        o3q     o3q        
    q3o             q3o    
o3o     q3q     q3q     o3o
            Q3o            
q3o     o3Q     o3Q     q3o
    q3q             q3q    
o3q     Q3o     Q3o     o3q
            o3Q            
o3o     q3q     q3q     o3o
    o3q             o3q    
        q3o     q3o        
            o3o           

            o3o            
                           
                           
o3o     q3q     q3q     o3o
                           
                           
    q3q             q3q    
                           
                           
o3o     q3q     q3q     o3o
                           
                           
            o3o           

         o3o         
                     
o3o   q3o   o3q   o3o
                     
   o3q         q3o   
                     
o3o   q3o   o3q   o3o
                     
         o3o         

This compound occurs in 6 different forms depending on whether the vertices (coincident by 2) will be counted separately (type A), or will be identified while the incident edges will still be counted separately (type C), or whether both would be identified (type E). All these would use 8 icositetrachora for compound components. – Each of those cases could be considered on base of the 4 icositetrachora compound (kitapna) instead, i.e. using just 2 such components. That then gives rise to (type B) with no identifications, (type D) with identification of vertices only, and (type F) with identifications of coincident vertices and concident edges.

How could this internal structure be understood? – Infact, there is a consistent 4-coloring of edges and faces for both, the oct and the ico: Just color opposite faces of an oct alike and use for each edge the 3 other colors: this then uses a chiral 3-ap coloring of the edges of oct. Next, as there are 3 incident faces per edge in ico, this oct coloring extends into an alike ico coloring also: for each colored edge use as incident face colorings the various other colors. Finally select one single of those colors and you'll have the special edges (which get doubled and thereafter identified in the compounding) as well as the special faces (with no such special edge being used for its boundary) well-defined. – Those special faces of bitapna are being highlighted in the picture of the vertex figure in light blue and gold.

Incidence matrix

(Type A) - no identifications

192 ♦   8 |  12 |   6 || 1  verf: cube
----+-----+-----+-----++--
  2 | 768 |   3 |   3 || 1
----+-----+-----+-----++--
  3 |   3 | 768 |   2 || 1
----+-----+-----+-----++--
  6 |  12 |   8 | 192 || 1  oct
----+-----+-----+-----++--
 24 |  96 |  96 |  24 || 8  ico

(Type B) - no identifications, but as 2 kitapna comp.

192 ♦   8 |  12 |   6 || 1  verf: cube
----+-----+-----+-----++--
  2 | 768 |   3 |   3 || 1
----+-----+-----+-----++--
  3 |   3 | 768 |   2 || 1
----+-----+-----+-----++--
  6 |  12 |   8 | 192 || 1  oct
----+-----+-----+-----++--
 96 | 384 | 384 |  96 || 2  kitapna

(Type C) - identifying incident vertices only 

96 |  16 |  24 |  12 || 2 verf: twirled vertex-first 2-cube comp. with no identifications
---+-----+-----+-----++--
 2 | 768 |   3 |   3 || 1
---+-----+-----+-----++--
 3 |   3 | 768 |   2 || 1
---+-----+-----+-----++--
 6 |  12 |   8 | 192 || 1  oct
---+-----+-----+-----++--
24 |  96 |  96 |  24 || 8  ico

(Type D) - identifying incident vertices only, but as 2 kitapna comp.

96 |  16 |  24 |  12 || 2 verf: twirled vertex-first 2-cube comp. with no identifications
---+-----+-----+-----++--
 2 | 768 |   3 |   3 || 1
---+-----+-----+-----++--
 3 |   3 | 768 |   2 || 1
---+-----+-----+-----++--
 6 |  12 |   8 | 192 || 1  oct
---+-----+-----+-----++--
96 | 384 | 384 |  96 || 2  kitapna

(Type E) - identifying vertices and coincident edges

96 |  2  12 |  18   6 |  12 || 2  verf: twirled vertex-first 2-cube comp. with identifications
---+--------+---------+-----++--
 2 | 96   * |   6   0 |   6 || 2  edge-fig: 2-{3} comp.
 2 |  * 576 |   2   1 |   3 || 1
---+--------+---------+-----++--
 3 |  1   2 | 576   * |   2 || 1
 3 |  0   3 |   * 192 |   2 || 1
---+--------+---------+-----++--
 6 |  3   9 |   6   2 | 192 || 1  oct (as chiral 3-aps)
---+--------+---------+-----++--
24 | 24  72 |  72  24 |  24 || 8  ico

(Type F) - identifying vertices and coincident edges, but as 2 kitapna comp.

96 |  2  12 |  18   6 |  12 || 2  verf: twirled vertex-first 2-cube comp. with identifications
---+--------+---------+-----++--
 2 | 96   * |   6   0 |   6 || 2  edge-fig: 2-{3} comp.
 2 |  * 576 |   2   1 |   3 || 1
---+--------+---------+-----++--
 3 |  1   2 | 576   * |   2 || 1
 3 |  0   3 |   * 192 |   2 || 1
---+--------+---------+-----++--
 6 |  3   9 |   6   2 | 192 || 1  oct (as chiral 3-aps)
---+--------+---------+-----++--
96 | 96 288 | 288  96 |  96 || 2  kitapna