Dodecateron

The dodecateron, also known by its OBSA dot, Coxeter symbol 0₂₂, is a uniform polyteron that is the birectification of the hexateron, composed of 12 rectified pentachora. Its vertex figure is a triangular duoprism. It has a circumradius of √32 ≈ 0.866025. Since it is isogonal and isotopal, it is considered noble.

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

Structure

Beginning on a rectified pentachoron, its octahedral cells join to 5 other rectified pentachora at an obtuse angle (≈101.5°), while its tetrahedral cells join to 5 other rectified pentachora at an acute angle (≈78.5°). This only leaves room for the opposite rectified pentachoron, completing the shape. All the non-base tera span the entire height of the shape. This structure is similar for all birectified simplices. From this perspective, the shape has a height of √155 ≈ 0.774597.

Beginning on a triangular duoprismatic vertex, 6 rectified pentachora are joined. Duplicating the cap, flipping it and double rotating it 180° yields the other 6 rectified pentachora, completing the shape. From this perspective, the shape has a height of √3 ≈ 1.732051.

Source: Incidence matrices — dot