Acronym bicypdex (alt.: bicypaugap) Name bi-cyclopentadiminished hexacosachoron,bi-cyclopentaaugmented great antiprism Circumradius (1+sqrt(5))/2 = 1.618034 Lace cityin 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)
```