1₄₂ polyzetton

The 1₄₂ polyzetton, also known as the 240-2160-zetton, long Greek diacosi­tessaraconta­dischilia­hecaton­hexeconta­zetton, OBSA bif, is a uniform polyzetton composed of 240 1₃₂ polyexa and 2160 demihepteracts. Its vertex figure is a birectified octaexon. It has a circumradius of 2.

Structure

Beginning on a 1₃₂ polyexon, its 1₂₂ polypeta join with 56 other 1₃₂ polyexa that touch the aequator while its demihexeracts join with 126 demihepteracts. This leaves gaps at its vertices, filled by 576 demihepteracts that touch the aequator. 126 aequatorial 3₂₁ polyexa are then placed after the first set of demihepteracts. 756 aequatorial demihepteracts are then placed in demipenteractic junctions corresponding to the base's demipenteracts. The structure mirrors past this point: 56 1₃₂ polyexa are placed after the first set and 576 demihepteracts are placed after the second set of demihepteracts. This then only leaves the opposite 1₃₂ polyexon, completing the shape. From this perspective, the shape has a height of 3.

Due to missing sources, its demihepteract- and vertex-first structures are unavailable. It can, however, be inferred these heights are, respectively, 5√22 ≈ 3.535534 and 4.

Having the same symmetry as the 2₄₁ polyzetton and 4₂₁ polyzetton, both with E₈ symmetry, their components have neat correspondences:

Source: Discord message — Klitzing, Lace city of bif