Demihepteract

The demihepteract, also known by its OBSA hesa, Coxeter symbol 1₄₁, is the alternation of the hepteract, composed of 14 demihexeracts and 32 heptapeta. Its vertex figure is a rectified heptapeton. It has a circumradius of 2√148 ≈ 0.935414.

It appears as a zetton of the 1₄₂ polyzetton as well as the vertex figure of the 2₄₁ polyzetton.

Structure

Beginning on a demihexeract, its triacontaditeral peta join to 12 other aequatorial demihexeracts, while its hexateral peta join to 32 heptapeta. This leaves gaps in the vertices filled by 32 heptapeta. This then only leaves the opposite demihexeract in inverse orientation, completing the shape. All the non-base exa span the entire height of the shape. This opposite demihexeract has its hexateral peta joined to the second set of heptapeta, while its vertices meet the first set. From this perspective, the shape has a height of √22 ≈ 0.707107.

Beginning on a heptapeton, all its hexateral peta join to 7 demihexeracts. This leaves gaps for 21 more heptapeta to be inserted at its edges and 7 more demihexeracts to be inserted at its vertices, which touch the opposite vertex. 35 heptapeta are then inserted into tetrahedral junctions corresponding to the base's tetrahedral cells. Finally, 7 heptapeta are placed after the first set of demihexeracts, completing the shape. From this perspective, the shape has a height of 3√147 ≈ 1.603567.

Source: Incidence matrices — hesa