# Truncated triangular prism

Truncated triangular prism
Rank3
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 ${\displaystyle {\frac {4{\sqrt {3}}}{9}}\approx 0.76980}$, one of length ${\displaystyle {\frac {10{\sqrt {3}}}{9}}\approx 1.92450}$, one of length ${\displaystyle {\frac {4{\sqrt {3}}}{3}}\approx 2.30940}$ and the other of length ${\displaystyle {\frac {5{\sqrt {3}}}{12}}\approx 0.72169}$. It has regular hexagons in place of ditrigons.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{3}},\,0,\,\pm {\frac {\sqrt {3}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),}$
• ${\displaystyle \left(0,\,1,\,\pm {\frac {\sqrt {3}}{4}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{4}}\right),}$

## Related polytopes

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