Penteractitriacontaditeron

The penteractitriacontaditeron, also known by its OBSA nit, Coxeter symbol 0₂₁₁, is a uniform polyteron that is the birectification of either the penteract or the triacontaditeron, as well as the rectification of the demipenteract, composed of 10 icositetrachora and 32 rectified pentachora. Its vertex figure is a triangular-square duoprism. It has a circumradius of √62 ≈ 1.224745.

It appears as a peton of the rectified 1₂₂ polypeton.

Structure

Beginning on an icositetrachoron, its tesseractic orbit cells join to 8 other aequatorial icositetrachora that span the entire height of the shape, while its hexadecachoral orbit cells join to 16 rectified pentachora. The aequator is a rectified tesseract; the cuboctahedra represent the halves of the icositetrachora while the pentachora represent the tetrahedral junctions between two rectified pentachora. The structure repeats past this point, with 16 more rectified pentachora placed after the first such set. This then only leaves space for the opposite icositetrachoron, completing the shape. From this perspective, the shape has a height of √2 ≈ 1.414214.

Beginning on a rectified pentachoron, its tetrahedral cells join to 5 other rectified pentachora, while its octahedral cells join to 5 icositetrachora that straddle the aequator. This leaves gaps at the vertices, filled by 10 rectified pentachora. 5 rectified pentachora are then placed after the first set of icositetrachora and likewise 5 icositetrachora are placed after the first set of rectified pentachora. 10 rectified pentachora are then placed at triangular junctions corresponding opposite the vertices of the base. This then only leaves the opposite rectified pentachoron, completing the shape. From this perspective, the shape has a height of 3√105 ≈ 1.897367.

Due to missing sources, its vertex-first structure is unavailable, although it can be inferred it has a height of √6 ≈ 2.449490.

Source: Incidence matrices — nit