# Truncated triangular prism

Truncated triangular prism Rank3
SpaceSpherical
Elements
Faces2 ditrigons, 3 rectangular-symmetric octagons, 6 isosceles triangles
Edges3+6+6+12
Vertices6+12
Vertex figures6 isosceles triangles
12 scalene triangles
Measures (edge length 1)
Central density1
Related polytopes
DualTriakis triangular tegum
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×A1, order 12
ConvexYes
NatureTame

The truncated triangular prism is a polyhedron formed by truncating the vertices of the triangular prism. It has 6 isosceles triangles, 3 rectangular-symmetric octagons and 2 ditrigons as faces.

The canonical variant with midradius 1 has four edge lengths: one of length $\frac{4\sqrt3}{9} ≈ 0.76980$ , one of length $\frac{10\sqrt3}{9} ≈ 1.92450$ , one of length $\frac{4\sqrt3}{3} ≈ 2.30940$ and the other of length $\frac{5\sqrt3}{12} ≈ 0.72169$ . It has regular hexagons in place of ditrigons.

## Vertex coordinates

The vertices of a canonical truncated triangular prism of midradius 1 are given by:

• $\left(±\frac{\sqrt3}{3},\,0,\,±\frac{\sqrt3}{2}\right),$ • $\left(±\frac{\sqrt3}{6},\,±\frac12,\,±\frac{\sqrt3}{2}\right),$ • $\left(0,\,1,\,±\frac{\sqrt3}{4}\right),$ • $\left(±\frac{\sqrt3}{2},\,-\frac12,\,±\frac{\sqrt3}{4}\right),$ ## Related polytopes

A variant of the truncated triangular prism with (A2×A1)+ symmetry occurs as the single cell-type of the tetraswirlic hexadecachoron.