Rectified hexateron

The rectified hexateron, also known by its OBSA rix, Coxeter symbol 0₃₁, is a uniform polyteron that is the rectification of the hexateron, composed of 6 rectified pentachora and 6 pentachora. Its vertex figure is a tetrahedral prism. It has a circumradius of √63 ≈ 0.816497.

It appears as a peton of the rectified heptapeton and the birectified heptapeton as well as the vertex figure of the demihexeract.

Structure

Beginning on a rectified pentachoron, its octahedral cells join to 5 other rectified pentachora, while its tetrahedral cells join to 5 pentachora. This only leaves room for the opposite pentachoron, completing the shape. All the non-base tera span the entire height of the shape. This opposite pentachoron has all its tetrahedral cells joined to rectified pentachora, with its vertices meeting other pentachora. This construction is similar for all rectified simplices. From this perspective, the shape has a height of √155 ≈ 0.774597.

Source: Incidence matrices — rix