D4.6 (EntityTopic, 15)

From Hi.gher. Space

Revision as of 23:35, 24 February 2014

CJ4.6 is a CRF polychoron crown jewel discovered by student91 on February 18, 2014. It is a modification of the hydrocantichoron o5x3o3x, where 30 rhodomesohedra are replaced by bilunabirotundae (J91), with the resulting non-CRF parts substituted by CRF patches containing 12 rosettes of 5 hexagonal prisms alternating with 5 truncated tetrahedra encircling pillars of pentagonal prisms capped by pentagonal rotundae.

Its construction is as follows: delete the vertices from o5x3o3x of edge length 2, whose first coordinate is less than the Golden Ratio φ or is equal to 2, then push the remaining vertices together (i.e., if the first coordinate is ≥φ then subtract φ; if it's ≤-φ then add φ). The vertices whose original first coordinates were φ become coincident. Then new points x5o3A are added with first coordinates ±1, where A=6φ. These modifications of o5x3o3x cause a reduction of its equatorial cells into 30 bilunabirotunda (J91s) in icosahedral symmetry, with the 12 gaps between them filled by circles of alternating hexagonal prisms and truncated tetrahedra surrounding a pentagonal prism with pentagonal cupolae above and below it. Twelve of the o5x3o's near the equatorial layer are truncated into pentagonal rotundae, and a number of stauromesohedra become triangular cupolae.

Projections

Side-view showing equatorial cells:

Top-view with highlighted equatorial cells:

Software model

• Stella4D .off file
• Polyview .def file