Acronym bicypdex (alt.: bicypaugap)
Name bi-cyclopentadiminished hexacosachoron,
bi-cyclopentaaugmented great antiprism
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
                          o5o                 
                   o5x                        
                                              
       x5o                     x5o            
o5o                                           
                   f5o                        
            o5f           o5f                 
                                              
o5x                                   o5x     
       f5o                     f5o            
                                              
                   x5o                     o5o
                                              
       o5f                     o5f            
x5o                                   x5o     
                                              
            f5o           f5o                 
                   o5f                        
o5o                                           
       o5x                     o5x            
                                              
                   x5o                        
                          o5o                 
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer
uniform relatives:
ex   gap  
related segmentochora:
pappy  

This polychoron either can be derived as a monostratic vertex diminishing at alternate vertices on 2 fully orthogonal great circles of ex. Any such diminishing introduces its vertex figure as new cell type, the ikes. Alternate vertices thereby just have the right distance so that those ikes just are placed tip-to-tip. – Alternatively bicypdex could be derived from gap by augmenting alternate paps by pappies. Thereby the introduced peppies pairwise become corealmic with the remaining paps and thus will join into ikes.

The references in the following incidence matrices therefore is based on the 4-coloring of gap: the yellow (y) and blue (b) paps become augmented, while the red (r) and green (g) ones thence become ikes.


Incidence matrix

5  *  * * | 10  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 10  5  5  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 2 10  0  0  0  0  0  0  0  0 0  0  r ike tip adjoins, verf = pap
* 50  * * |  1  2  1  1  1  1  1  1  1  1  0  0  0  0  0  0 |  2  1  1  3  3  2  2  2  2  2  1  1  1  1  1  0  0  0  0  0 | 1  3  3  3  1  1  1  1  1  1 0  0  verf = gyepip
*  * 50 * |  0  0  0  0  0  0  1  1  1  1  1  1  1  1  2  1 |  0  0  0  0  0  1  1  1  1  1  2  2  2  2  2  3  3  1  1  2 | 0  0  1  1  1  1  1  1  3  3 1  3  verf = gyepip
*  *  * 5 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 10 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  5  5 10 | 0  0  0  0  0  0  0  0  0  0 2 10  g ike tip adjoins, verf = pap
----------+-------------------------------------------------+-------------------------------------------------------------+----------------------------------
1  1  0 0 | 50  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  2  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  3  0  0  0  0  0  0  0  0 0  0  polar edges of r ikes
0  2  0 0 |  * 50  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  1  0  0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  1  1  1  0  0  0  0  0  0 0  0  tropal edges of r ikes
0  2  0 0 |  *  * 25  *  *  *  *  *  *  *  *  *  *  *  *  * |  0  0  0  2  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  0  2  0  1  0  0  0  0  0 0  0  meandric r/g edges of r ikes
0  2  0 0 |  *  *  * 25  *  *  *  *  *  *  *  *  *  *  *  * |  0  0  0  2  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0 | 1  0  2  0  0  1  0  0  0  0 0  0  meandric r/b edges of r ikes
0  2  0 0 |  *  *  *  * 25  *  *  *  *  *  *  *  *  *  *  * |  0  1  0  0  2  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0 | 0  2  0  2  0  0  1  0  0  0 0  0  toroidal y/g edges of r ring
0  2  0 0 |  *  *  *  *  * 25  *  *  *  *  *  *  *  *  *  * |  0  0  1  0  2  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0 | 0  2  0  2  0  0  0  1  0  0 0  0  toroidal y/b edges of r ring
0  1  1 0 |  *  *  *  *  *  * 50  *  *  *  *  *  *  *  *  * |  0  0  0  0  0  1  1  0  1  0  1  1  0  0  0  0  0  0  0  0 | 0  0  1  1  1  0  1  0  1  0 0  0  ry/g joining edges
0  1  1 0 |  *  *  *  *  *  *  * 50  *  *  *  *  *  *  *  * |  0  0  0  0  0  1  0  1  0  1  0  0  1  1  0  0  0  0  0  0 | 0  0  1  1  0  1  0  1  0  1 0  0  ry/b joining edges
0  1  1 0 |  *  *  *  *  *  *  *  * 50  *  *  *  *  *  *  * |  0  0  0  0  0  0  1  1  0  0  1  0  1  0  1  0  0  0  0  0 | 0  0  1  0  1  1  0  0  1  1 0  0  r/gb joining edges
0  1  1 0 |  *  *  *  *  *  *  *  *  * 50  *  *  *  *  *  * |  0  0  0  0  0  0  0  0  1  1  0  1  0  1  1  0  0  0  0  0 | 0  0  0  1  0  0  1  1  1  1 0  0  y/gb joining edges
0  0  2 0 |  *  *  *  *  *  *  *  *  *  * 25  *  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0 | 0  0  0  0  1  0  0  0  2  0 1  0  meandric g/r edges of g ikes
0  0  2 0 |  *  *  *  *  *  *  *  *  *  *  * 25  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0 | 0  0  0  0  0  0  1  0  0  2 1  0  meandric g/y edges of g ikes
0  0  2 0 |  *  *  *  *  *  *  *  *  *  *  *  * 25  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  1  0  0 | 0  0  0  0  0  1  0  0  2  0 0  2  toroidal b/r edges of g ring
0  0  2 0 |  *  *  *  *  *  *  *  *  *  *  *  *  * 25  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  1  0 | 0  0  0  0  0  0  0  1  0  2 0  2  toroidal b/y edges of g ring
0  0  2 0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 50  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  0  0  1 | 0  0  0  0  0  0  0  0  1  1 1  1  tropal edges of g ikes
0  0  1 1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 50 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  2 | 0  0  0  0  0  0  0  0  0  0 1  3  polar edges of g ikes
----------+-------------------------------------------------+-------------------------------------------------------------+----------------------------------
1  2  0 0 |  2  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 50  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  1  0  0  0  0  0  0  0  0 0  0  atop tropal edges of r ikes
1  2  0 0 |  2  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0 |  * 25  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  2  0  0  0  0  0  0  0  0 0  0  atop toroidal y/g edges of r ring
1  2  0 0 |  2  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0 |  *  * 25  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  2  0  0  0  0  0  0  0  0 0  0  atop toroidal y/b edges of r ring
0  3  0 0 |  0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0 |  *  *  * 50  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  1  0  0  0  0  0  0  0 0  0  r/gb
0  3  0 0 |  0  1  0  0  1  1  0  0  0  0  0  0  0  0  0  0 |  *  *  *  * 50  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1  0  1  0  0  0  0  0  0 0  0  y/gb
0  2  1 0 |  0  1  0  0  0  0  1  1  0  0  0  0  0  0  0  0 |  *  *  *  *  * 50  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  0  1  1  0  0  0  0  0  0 0  0  extending tropal edges of r ikes
0  2  1 0 |  0  0  1  0  0  0  1  0  1  0  0  0  0  0  0  0 |  *  *  *  *  *  * 50  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  0  1  0  1  0  0  0  0  0 0  0  adjoined to meandric r/g edges of r ikes
0  2  1 0 |  0  0  0  1  0  0  0  1  1  0  0  0  0  0  0  0 |  *  *  *  *  *  *  * 50  *  *  *  *  *  *  *  *  *  *  *  * | 0  0  1  0  0  1  0  0  0  0 0  0  adjoined to meandric r/b edges of r ikes
0  2  1 0 |  0  0  0  0  1  0  1  0  0  1  0  0  0  0  0  0 |  *  *  *  *  *  *  *  * 50  *  *  *  *  *  *  *  *  *  *  * | 0  0  0  1  0  0  1  0  0  0 0  0  adjoined to toroidal y/g edges of r ring
0  2  1 0 |  0  0  0  0  0  1  0  1  0  1  0  0  0  0  0  0 |  *  *  *  *  *  *  *  *  * 50  *  *  *  *  *  *  *  *  *  * | 0  0  0  1  0  0  0  1  0  0 0  0  adjoined to toroidal y/b edges of r ring
0  1  2 0 |  0  0  0  0  0  0  1  0  1  0  1  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  * 50  *  *  *  *  *  *  *  *  * | 0  0  0  0  1  0  0  0  1  0 0  0  adjoined to meandric g/r edges of g ikes
0  1  2 0 |  0  0  0  0  0  0  1  0  0  1  0  1  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  * 50  *  *  *  *  *  *  *  * | 0  0  0  0  0  1  0  0  0  1 0  0  adjoined to meandric g/y edges of g ikes
0  1  2 0 |  0  0  0  0  0  0  0  1  1  0  0  0  1  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  * 50  *  *  *  *  *  *  * | 0  0  0  0  0  0  1  0  1  0 0  0  adjoined to toroidal b/r edges of g ring
0  1  2 0 |  0  0  0  0  0  0  0  1  0  1  0  0  0  1  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  * 50  *  *  *  *  *  * | 0  0  0  0  0  0  0  1  0  1 0  0  adjoined to toroidal b/y edges of g ring
0  1  2 0 |  0  0  0  0  0  0  0  0  1  1  0  0  0  0  1  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 50  *  *  *  *  * | 0  0  0  0  0  0  0  0  1  1 0  0  extending tropal edges of g ikes
0  0  3 0 |  0  0  0  0  0  0  0  0  0  0  1  0  1  0  1  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 50  *  *  *  * | 0  0  0  0  0  0  0  0  1  0 1  0  g/ry
0  0  3 0 |  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 50  *  *  * | 0  0  0  0  0  0  0  0  0  1 0  1  b/ry
0  0  2 1 |  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 25  *  * | 0  0  0  0  0  0  0  0  0  0 0  2  atop toroidal b/r edges of g ring
0  0  2 1 |  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 25  * | 0  0  0  0  0  0  0  0  0  0 0  2  atop toroidal b/y edges of g ring
0  0  2 1 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 50 | 0  0  0  0  0  0  0  0  0  0 1  1  atop tropal edges of g ikes
----------+-------------------------------------------------+-------------------------------------------------------------+----------------------------------
2 10  0 0 | 10 10  5  5  0  0  0  0  0  0  0  0  0  0  0  0 | 10  0  0 10  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 5  *  *  *  *  *  *  *  *  * *  *  r ike
1  3  0 0 |  3  1  0  0  1  1  0  0  0  0  0  0  0  0  0  0 |  1  1  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | * 50  *  *  *  *  *  *  *  * *  *  tet atop y/gb
0  3  1 0 |  0  1  1  1  0  0  1  1  1  0  0  0  0  0  0  0 |  0  0  0  1  0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0 | *  * 50  *  *  *  *  *  *  * *  *  r/gb tet(adj)
0  3  1 0 |  0  1  0  0  1  1  1  1  0  1  0  0  0  0  0  0 |  0  0  0  0  1  1  0  0  1  1  0  0  0  0  0  0  0  0  0  0 | *  *  * 50  *  *  *  *  *  * *  *  y/gb tet(adj)
0  2  2 0 |  0  0  1  0  0  0  2  0  2  0  1  0  0  0  0  0 |  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  0  0  0 | *  *  *  * 25  *  *  *  *  * *  *  rg tet(isol)
0  2  2 0 |  0  0  0  1  0  0  0  2  2  0  0  0  1  0  0  0 |  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  0 | *  *  *  *  * 25  *  *  *  * *  *  rb tet(isol)
0  2  2 0 |  0  0  0  0  1  0  2  0  0  2  0  1  0  0  0  0 |  0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  0  0  0 | *  *  *  *  *  * 25  *  *  * *  *  yg tet(isol)
0  2  2 0 |  0  0  0  0  0  1  0  2  0  2  0  0  0  1  0  0 |  0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  0 | *  *  *  *  *  *  * 25  *  * *  *  yb tet(isol)
0  1  3 0 |  0  0  0  0  0  0  1  0  1  1  1  0  1  0  1  0 |  0  0  0  0  0  0  0  0  0  0  1  0  1  0  1  1  0  0  0  0 | *  *  *  *  *  *  *  * 50  * *  *  g/ry tet(adj)
0  1  3 0 |  0  0  0  0  0  0  0  1  1  1  0  1  0  1  1  0 |  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1  0  1  0  0  0 | *  *  *  *  *  *  *  *  * 50 *  *  b/ry tet(adj)
0  0 10 2 |  0  0  0  0  0  0  0  0  0  0  5  5  0  0 10 10 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 10  0  0  0 10 | *  *  *  *  *  *  *  *  *  * 5  *  g ike
0  0  3 1 |  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  3 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  1 | *  *  *  *  *  *  *  *  *  * * 50  tet atop b/ry
or
10   * |  10   0  0  0  0  0   0   0 |  10  5  5   0   0   0   0   0   0   0 |  2  10   0   0  0  0  0  ike tip adjoins, verf = pap
 * 100 |   1   2  1  1  1  1   2   2 |   2  1  1   3   3   3   3   3   3   3 |  1   3   4   4  1  2  1  verf = gyepip
-------+-----------------------------+---------------------------------------+------------------------
 1   1 | 100   *  *  *  *  *   *   * |   2  1  1   0   0   0   0   0   0   0 |  1   3   0   0  0  0  0  polar edges of ikes
 0   2 |   * 100  *  *  *  *   *   * |   1  0  0   1   1   1   0   0   0   0 |  1   1   1   1  0  0  0  tropal edges of ikes
 0   2 |   *   * 50  *  *  *   *   * |   0  0  0   2   0   0   2   0   0   0 |  1   0   2   0  1  0  0  meandric r/g + g/r edges
 0   2 |   *   *  * 50  *  *   *   * |   0  0  0   2   0   0   0   2   0   0 |  1   0   2   0  0  1  0  meandric r/b + g/y edges
 0   2 |   *   *  *  * 50  *   *   * |   0  1  0   0   2   0   0   0   2   0 |  0   2   0   2  0  1  0  toroidal y/g + b/r edges
 0   2 |   *   *  *  *  * 50   *   * |   0  0  1   0   2   0   0   0   0   2 |  0   2   0   2  0  0  1  toroidal y/b + b/y edges
 0   2 |   *   *  *  *  *  * 100   * |   0  0  0   0   0   1   2   1   1   0 |  0   0   2   1  1  1  0  ry/g + gb/r joining edges
 0   2 |   *   *  *  *  *  *   * 100 |   0  0  0   0   0   1   0   1   1   2 |  0   0   1   2  0  1  1  ry/b + gb/y joining edges
-------+-----------------------------+---------------------------------------+------------------------
 1   2 |   2   1  0  0  0  0   0   0 | 100  *  *   *   *   *   *   *   *   * |  1   1   0   0  0  0  0  atop tropal edges of ikes
 1   2 |   2   0  0  0  1  0   0   0 |   * 50  *   *   *   *   *   *   *   * |  0   2   0   0  0  0  0  atop toroidal y/g + b/r edges of rings
 1   2 |   2   0  0  0  0  1   0   0 |   *  * 50   *   *   *   *   *   *   * |  0   2   0   0  0  0  0  atop toroidal y/b edges of rings
 0   3 |   0   1  1  1  0  0   0   0 |   *  *  * 100   *   *   *   *   *   * |  1   0   1   0  0  0  0  r/gb + g/ry
 0   3 |   0   1  0  0  1  1   0   0 |   *  *  *   * 100   *   *   *   *   * |  0   1   0   1  0  0  0  y/gb + b/ry
 0   3 |   0   1  0  0  0  0   1   1 |   *  *  *   *   * 100   *   *   *   * |  0   0   1   1  0  0  0  extending tropal edges of ikes
 0   3 |   0   0  1  0  0  0   2   0 |   *  *  *   *   *   * 100   *   *   * |  0   0   1   0  1  0  0  adjoined to meandric r/g + g/r edges
 0   3 |   0   0  0  1  0  0   1   1 |   *  *  *   *   *   *   * 100   *   * |  0   0   1   0  0  1  0  adjoined to meandric r/b + g/y edges
 0   3 |   0   0  0  0  1  0   1   1 |   *  *  *   *   *   *   *   * 100   * |  0   0   0   1  0  1  0  adjoined to toroidal y/g + b/r edges
 0   3 |   0   0  0  0  0  1   0   2 |   *  *  *   *   *   *   *   *   * 100 |  0   0   0   1  0  0  1  adjoined to toroidal y/b + b/y edges
-------+-----------------------------+---------------------------------------+------------------------
 2  10 |  10  10  5  5  0  0   0   0 |  10  0  0  10   0   0   0   0   0   0 | 10   *   *   *  *  *  *  ike
 1   3 |   3   1  0  0  1  1   0   0 |   1  1  1   0   1   0   0   0   0   0 |  * 100   *   *  *  *  *  tet atop y/gb + b/ry
 0   4 |   0   1  1  1  0  0   2   1 |   0  0  0   1   0   1   1   1   0   0 |  *   * 100   *  *  *  *  r/gb + g/ry tet(adj)
 0   4 |   0   1  0  0  1  1   1   2 |   0  0  0   0   1   1   0   0   1   1 |  *   *   * 100  *  *  *  y/gb + b/ry tet(adj)
 0   4 |   0   0  2  0  0  0   4   0 |   0  0  0   0   0   0   4   0   0   0 |  *   *   *   * 25  *  *  rg tet(isol)
 0   4 |   0   0  0  1  1  0   2   2 |   0  0  0   0   0   0   0   2   2   0 |  *   *   *   *  * 50  *  rb + yg tet(isol)
 0   4 |   0   0  0  0  0  2   0   4 |   0  0  0   0   0   0   0   0   0   4 |  *   *   *   *  *  * 25  yb tet(isol)

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