Acronym pybiscrox Name pyritohedral bistratic icosahedron-first cap of rectified hexacosachoron Circumradius sqrt[5+2 sqrt(5)] = 3.077684 Lace cityin approx. ASCII-art x2o o2f f2x o2f x2o -- ike x2f F2x f2F f2F F2x x2f -- id \ fq-oct x2x o2F F2f Af2oV V2F xB2Bx F2A xB2Bx V2F Af2oV F2f o2F x2x -- srid _ -_ +-- pip where: F=ff=f+x, V=2f, A=F+x=f+u=f+2x, B=V+x=2f+x Confer uniform relative: rox   related CRFs: biscrox   doe || (id \ fq-oct) || f-ike || doe

This polychoron is obtained from biscrox, the bistratic ike-first cap of rox, by means of the observation that the vertex figure of rox is pip. Although not all vertices could be such diminished without producing mutual intersections and without leaving the realm of CRFs, it well is possible to do so only within the medial layer and even there with pyritohedral subsymmetry only. In fact, it was obtained at the beginning of 2021 by a guy calling himself "puffer fish" by applying that diminishing at those vertices of the medial layer id which correspond to a vertex-inscribed fq-oct only.

Incidence matrix

ike || pseudo (id \ fq-oct) || srid   → height(1,2) = (sqrt(5)-1)/4 = 0.309017
height(2,3) = 1/2

12  *  *  *  * | 1  4  2  2  0  0  0  0  0  0  0  0  0  0  0  0 |  3 2  4  2  1  2  1 0  0  0  0  0  0  0  0 0  0  0  0 0 | 1  3 2 1  1 0  0  0 0  top layer
* 24  *  *  * | 0  0  1  1  1  2  1  1  1  1  0  0  0  0  0  0 |  0 0  1  1  1  2  1 1  1  1  2  1  1  1  1 0  0  0  0 0 | 0  1 1 1  2 1  1  1 0  equatorial layer
*  * 24  *  * | 0  0  0  0  0  0  1  0  0  0  1  1  1  1  0  0 |  0 0  0  0  0  0  1 0  1  0  0  1  1  0  0 1  1  1  1 0 | 0  0 0 1  1 0  1  1 1  vertices of octahedrally situated {4} of bottom layer (A)
*  *  * 12  * | 0  0  0  0  0  0  0  2  0  0  0  0  2  0  2  0 |  0 0  0  0  0  0  0 0  0  1  0  2  0  2  0 0  1  1  2 0 | 0  0 0 0  1 0  1  2 1  tip-vertices of adjacent {3} of bottom layer (B)
*  *  *  * 24 | 0  0  0  0  0  0  0  0  1  1  0  0  0  1  1  2 |  0 0  0  0  0  0  0 0  0  0  1  0  1  1  2 0  0  1  2 1 | 0  0 0 0  1 1  0  2 1  vertices of cubical situated {3} of bottom layer (C)
---------------+------------------------------------------------+---------------------------------------------------------+----------------------
2  0  0  0  0 | 6  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  2 0  0  2  0  0  0 0  0  0  0  0  0  0  0 0  0  0  0 0 | 1  2 0 1  0 0  0  0 0  octahedrally situated edges of top layer
2  0  0  0  0 | * 24  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  1 1  1  0  0  0  0 0  0  0  0  0  0  0  0 0  0  0  0 0 | 1  1 1 0  0 0  0  0 0  other edges of top layer
1  1  0  0  0 | *  * 24  *  *  *  *  *  *  *  *  *  *  *  *  * |  0 0  1  1  0  1  1 0  0  0  0  0  0  0  0 0  0  0  0 0 | 0  1 1 1  1 0  0  0 0  upper edges along the pips
1  1  0  0  0 | *  *  * 24  *  *  *  *  *  *  *  *  *  *  *  * |  0 0  1  0  1  1  0 0  0  0  0  0  0  0  0 0  0  0  0 0 | 0  1 1 0  1 0  0  0 0  other upper edges
0  2  0  0  0 | *  *  *  * 12  *  *  *  *  *  *  *  *  *  *  * |  0 0  0  1  1  0  0 0  1  1  0  0  0  0  0 0  0  0  0 0 | 0  1 0 1  1 0  1  0 0  base-edges of former {5} of medial layer
0  2  0  0  0 | *  *  *  *  * 24  *  *  *  *  *  *  *  *  *  * |  0 0  0  0  0  1  0 1  0  0  1  0  0  0  0 0  0  0  0 0 | 0  0 1 0  1 1  0  0 0  edges of remaining {3} of medial layer
0  1  1  0  0 | *  *  *  *  *  * 24  *  *  *  *  *  *  *  *  * |  0 0  0  0  0  0  1 0  1  0  0  1  1  0  0 0  0  0  0 0 | 0  0 0 1  1 0  1  1 0
0  1  0  1  0 | *  *  *  *  *  *  * 24  *  *  *  *  *  *  *  * |  0 0  0  0  0  0  0 0  0  1  0  1  0  1  0 0  0  0  0 0 | 0  0 0 0  1 0  1  1 0
0  1  0  0  1 | *  *  *  *  *  *  *  * 24  *  *  *  *  *  *  * |  0 0  0  0  0  0  0 0  0  0  1  0  1  0  1 0  0  0  0 0 | 0  0 0 0  1 1  0  1 0  leaning towards the (A) bottom vertex
0  1  0  0  1 | *  *  *  *  *  *  *  *  * 24  *  *  *  *  *  * |  0 0  0  0  0  0  0 0  0  0  1  0  0  1  1 0  0  0  0 0 | 0  0 0 0  1 1  0  1 0  leaning towards the (B) bottom vertex
0  0  2  0  0 | *  *  *  *  *  *  *  *  *  * 12  *  *  *  *  * |  0 0  0  0  0  0  0 0  1  0  0  0  0  0  0 1  1  0  0 0 | 0  0 0 1  0 0  1  0 1  connecting {3} and {4} in bottom layer
0  0  2  0  0 | *  *  *  *  *  *  *  *  *  *  * 12  *  *  *  * |  0 0  0  0  0  0  1 0  0  0  0  0  0  0  0 1  0  1  0 0 | 0  0 0 1  1 0  0  0 1  connecting {4} and {5} in bottom layer
0  0  1  1  0 | *  *  *  *  *  *  *  *  *  *  *  * 24  *  *  * |  0 0  0  0  0  0  0 0  0  0  0  1  0  0  0 0  1  0  1 0 | 0  0 0 0  0 0  1  1 1
0  0  1  0  1 | *  *  *  *  *  *  *  *  *  *  *  *  * 24  *  * |  0 0  0  0  0  0  0 0  0  0  0  0  1  0  0 0  0  1  1 0 | 0  0 0 0  1 0  0  1 1
0  0  0  1  1 | *  *  *  *  *  *  *  *  *  *  *  *  *  * 24  * |  0 0  0  0  0  0  0 0  0  0  0  0  0  1  0 0  0  1  1 0 | 0  0 0 0  1 0  0  1 1
0  0  0  0  2 | *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 24 |  0 0  0  0  0  0  0 0  0  0  0  0  0  0  1 0  0  0  1 1 | 0  0 0 0  0 1  0  1 1
---------------+------------------------------------------------+---------------------------------------------------------+----------------------
3  0  0  0  0 | 1  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 12 *  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  * * | 1  1 0 0  0 0  0  0 0  {3} adjacent to octahedrally situated edges of top layer
3  0  0  0  0 | 0  3  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |  * 8  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  * * | 1  0 1 0  0 0  0  0 0  cubical situated {3} of top layer
2  1  0  0  0 | 0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0 |  * * 24  *  *  *  * *  *  *  *  *  *  *  * *  *  *  * * | 0  1 1 0  0 0  0  0 0
2  2  0  0  0 | 1  0  2  0  1  0  0  0  0  0  0  0  0  0  0  0 |  * *  * 12  *  *  * *  *  *  *  *  *  *  * *  *  *  * * | 0  1 0 1  0 0  0  0 0
1  2  0  0  0 | 0  0  0  2  1  0  0  0  0  0  0  0  0  0  0  0 |  * *  *  * 12  *  * *  *  *  *  *  *  *  * *  *  *  * * | 0  1 0 0  1 0  0  0 0  adjoining the base-edges of former {5} of medial layer
1  2  0  0  0 | 0  0  1  1  0  1  0  0  0  0  0  0  0  0  0  0 |  * *  *  *  * 24  * *  *  *  *  *  *  *  * *  *  *  * * | 0  0 1 0  1 0  0  0 0  adjoining the edges of remaining {3} of medial layer
1  2  2  0  0 | 0  0  2  0  0  0  2  0  0  0  0  1  0  0  0  0 |  * *  *  *  *  * 12 *  *  *  *  *  *  *  * *  *  *  * * | 0  0 0 1  1 0  0  0 0
0  3  0  0  0 | 0  0  0  0  0  3  0  0  0  0  0  0  0  0  0  0 |  * *  *  *  *  *  * 8  *  *  *  *  *  *  * *  *  *  * * | 0  0 1 0  0 1  0  0 0
0  2  2  0  0 | 0  0  0  0  1  0  2  0  0  0  1  0  0  0  0  0 |  * *  *  *  *  *  * * 12  *  *  *  *  *  * *  *  *  * * | 0  0 0 1  0 0  1  0 0
0  2  0  1  0 | 0  0  0  0  1  0  0  2  0  0  0  0  0  0  0  0 |  * *  *  *  *  *  * *  * 12  *  *  *  *  * *  *  *  * * | 0  0 0 0  1 0  1  0 0
0  2  0  0  1 | 0  0  0  0  0  1  0  0  1  1  0  0  0  0  0  0 |  * *  *  *  *  *  * *  *  * 24  *  *  *  * *  *  *  * * | 0  0 0 0  1 1  0  0 0
0  1  1  1  0 | 0  0  0  0  0  0  1  1  0  0  0  0  1  0  0  0 |  * *  *  *  *  *  * *  *  *  * 24  *  *  * *  *  *  * * | 0  0 0 0  0 0  1  1 0
0  1  1  0  1 | 0  0  0  0  0  0  1  0  1  0  0  0  0  1  0  0 |  * *  *  *  *  *  * *  *  *  *  * 24  *  * *  *  *  * * | 0  0 0 0  1 0  0  1 0
0  1  0  1  1 | 0  0  0  0  0  0  0  1  0  1  0  0  0  0  1  0 |  * *  *  *  *  *  * *  *  *  *  *  * 24  * *  *  *  * * | 0  0 0 0  1 0  0  1 0
0  1  0  0  2 | 0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  1 |  * *  *  *  *  *  * *  *  *  *  *  *  * 24 *  *  *  * * | 0  0 0 0  0 1  0  1 0
0  0  4  0  0 | 0  0  0  0  0  0  0  0  0  0  2  2  0  0  0  0 |  * *  *  *  *  *  * *  *  *  *  *  *  *  * 6  *  *  * * | 0  0 0 1  0 0  0  0 1
0  0  2  1  0 | 0  0  0  0  0  0  0  0  0  0  1  0  2  0  0  0 |  * *  *  *  *  *  * *  *  *  *  *  *  *  * * 12  *  * * | 0  0 0 0  0 0  1  0 1
0  0  2  1  2 | 0  0  0  0  0  0  0  0  0  0  0  1  0  2  2  0 |  * *  *  *  *  *  * *  *  *  *  *  *  *  * *  * 12  * * | 0  0 0 0  1 0  0  0 1
0  0  1  1  2 | 0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  1 |  * *  *  *  *  *  * *  *  *  *  *  *  *  * *  *  * 24 * | 0  0 0 0  0 0  0  1 1
0  0  0  0  3 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  3 |  * *  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  * 8 | 0  0 0 0  0 1  0  0 1
---------------+------------------------------------------------+---------------------------------------------------------+----------------------
12  0  0  0  0 | 6 24  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 12 8  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0  0  0 0 | 1  * * *  * *  *  * *  top ike
3  2  0  0  0 | 1  2  2  2  1  0  0  0  0  0  0  0  0  0  0  0 |  1 0  2  1  1  0  0 0  0  0  0  0  0  0  0 0  0  0  0 0 | * 12 * *  * *  *  * *  top squippy
3  3  0  0  0 | 0  3  3  3  0  3  0  0  0  0  0  0  0  0  0  0 |  0 1  3  0  0  3  0 1  0  0  0  0  0  0  0 0  0  0  0 0 | *  * 8 *  * *  *  * *  top oct
2  4  4  0  0 | 1  0  4  0  2  0  4  0  0  0  2  2  0  0  0  0 |  0 0  0  2  0  0  2 0  2  0  0  0  0  0  0 1  0  0  0 0 | *  * * 6  * *  *  * *  pip
1  4  2  1  2 | 0  0  2  2  1  2  2  2  2  2  0  1  0  2  2  0 |  0 0  0  0  1  2  1 0  0  1  2  0  2  2  0 0  0  1  0 0 | *  * * * 12 *  *  * *  mibdi
0  3  0  0  3 | 0  0  0  0  0  3  0  0  3  3  0  0  0  0  0  3 |  0 0  0  0  0  0  0 1  0  0  3  0  0  0  3 0  0  0  0 1 | *  * * *  * 8  *  * *  bottom oct
0  2  2  1  0 | 0  0  0  0  1  0  2  2  0  0  1  0  2  0  0  0 |  0 0  0  0  0  0  0 0  1  1  0  2  0  0  0 0  1  0  0 0 | *  * * *  * * 12  * *  bottom squippy
0  1  1  1  2 | 0  0  0  0  0  0  1  1  1  1  0  0  1  1  1  1 |  0 0  0  0  0  0  0 0  0  0  0  1  1  1  1 0  0  0  1 0 | *  * * *  * *  * 24 *  remaining base squippy
0  0 24 12 24 | 0  0  0  0  0  0  0  0  0  0 12 12 24 24 24 24 |  0 0  0  0  0  0  0 0  0  0  0  0  0  0  0 6 12 12 24 8 | *  * * *  * *  *  * 1  base srid