Triangular triswirlprism

The triangular triswirlprism is a convex isogonal polychoron that consists of 18 triangular antiprisms and 54 phyllic disphenoids. It is the simplest nontrivial member of the duoprismatic swirlprisms. Together with its dual, it is the eighth in an infinite family of triangular dihedral swirlchora.

Vertex coordinates
The vertices of a triangular triswirlprism, constructed as the convex hull of three 3-3 duoprisms of edge length 1, centered at the origin, are given by:


 * (0, $\sqrt{3}$/3, 0, $\sqrt{3}$/3),
 * (0, $\sqrt{3}$/3, ±1/2, –$\sqrt{3}$/6),
 * (±1/2, –$\sqrt{3}$/6, 0, $\sqrt{3}$/3),
 * (±1/2, –$\sqrt{3}$/6, ±1/2, –$\sqrt{3}$/6),
 * ($\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, $\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * ($\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, $\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * ($\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, –$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3)
 * ($\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, $\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * ($\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, $\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * ($\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, –$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * (–$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, $\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * (–$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, $\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * (–$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, –$\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * ($\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, $\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * ($\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, –$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * ($\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3, –$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * (–$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, $\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * (–$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, –$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * (–$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3, –$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3),
 * (–$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, $\sqrt{3}$cos(π/18)/3, $\sqrt{3}$sin(π/18)/3),
 * (–$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, –$\sqrt{3}$sin(π/9)/3, –$\sqrt{3}$cos(π/9)/3),
 * (–$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3, –$\sqrt{3}$sin(2π/9)/3, $\sqrt{3}$cos(2π/9)/3).