2₄₁ polyzetton

The 2₄₁ polyzetton, also known as the 240-17280-zetton, long Greek diacosi­tessaraconta­myria­heptachilia­diacos­ogdoëconta­zetton, OBSA bay, is a uniform polyzetton composed of 240 2₃₁ polyexa and 17280 octaexa. Its vertex figure is a demihepteract. It has a circumradius of √2 ≈ 1.414214.

Structure

Beginning from a 2₃₁ polyexon, its 2₂₁ polypeta join to 56 other 2₃₁ polyexa that touch the aequator, while its heptapeta join to 576 octaexa. This leaves gaps at its edges, filled by 2016 octaexa, and at its vertices, filled by 126 aequatorial 2₃₁ polyexa that span the entire height of the shape. 4032 octaexa that touch the aequator are then placed at pentachoral junctions corresponding to the triangular faces of the base. Likewise, another 4032 aequatorial octaexa are placed askew at vertex junctions corresponding to the vertices of a demified 3₂₁ polyexon. The structure mirrors past this point: 56 2₃₁ polyexa are added after the first set, 4032 octaexa are placed at aequatorial triangular junctions after the second previous set, 4032 octaexa are placed in hexateral junctions corresponding to the base's edges and 576 octaexa are placed in vertex junctions corresponding to the base's octaexa. This then only leaves room for the opposite 2₃₁ polyexon, completing the shape. From this perspective, the shape has a height of 2.

Due to missing sources, its octaexon- and vertex-first structures are unavailable. It can, however, be inferred these heights, are, respectively, 52 = 2.5 and 2√2 ≈ 2.828427.

Having the same symmetry as the 1₄₂ polyzetton and 4₂₁ polyzetton, both with E₈ symmetry, their components have neat correspondences:

Source: Incidence matrices — bay