Triangular-antitegmatic icosachoron

The triangular-antitegmatic icosachoron is a convex isochoric polychoron with 20 triangular antitegums as cells It can be obtained as the dual of the small prismatodecachoron.

It can also be constructed as the convex hull of 2 dual pentachora and 2 opposite rectified pentachora, all of the same edge length. Related to this fact is that it is the 4D vertex-first projection of the regular 5-cube, or in other words, it is the Minkowski sum of 5 line segments from the center to vertices of a pentachoron. This makes it a zonochoron.

Each face of this polyhedron is a rhombus with acute angle $$\arccos\left(\frac14\right) ≈ 75.52249°$$ and obtuse angle $$\arccos\left(-\frac14\right) ≈ 104.47751°$$.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular antitegum (20): Small prismatodecachoron
 * Rhombus (60): Rectified small prismatodecachoron
 * Edge (30): Decachoron
 * Edge (40): Bitruncatodecachoron
 * Vertex (10): Bidecachoron
 * Vertex (20): Biambodecachoron