Demipenteract

The demipenteract, also known by its OBSA hin, Coxeter symbol 1₂₁, is the alternation of the penteract, composed of 10 hexadecachora and 16 pentachora. Its vertex figure is a rectified pentachoron. It has a circumradius of 2√108 ≈ 0.790569. Just like any odd demicube, it has a vertex opposite a simplicial facet.

It appears as a peton of the 1₂₂ polypeton as well as the vertex figure of the 2₂₁ polypeton.

Structure

Beginning on a hexadecachoron, half of the tetrahedral cells join to 8 pentachora while the other half join to 8 other aequatorial hexadecachora. This leaves a gap at each vertex where 8 pentachora are inserted. This then only leaves the opposite hexadecachoron in inverse orientation, completing the shape. All the non-base tera span the entire height of the shape. This opposite hexadecachoron has half of its tetrahedral cells joined to the second set of pentachora, while its vertices meet the first set. This structure is similar for all demicubes. From this perspective, the shape has a height of √22 ≈ 0.707107.

Beginning on a pentachoron, all its tetrahedral cells join to 5 hexadecachora. This leaves gaps for 10 pentachora to be inserted at its edges and 5 hexadecachora that bridge across the height of the shape to be inserted at its vertices. 5 pentachora are placed after the former set of hexadecachora, which complete the opposite vertex. From this perspective, the shape has a height of 2√105 ≈ 1.264911.

Source: Incidence matrices — hin