Truncated triangular prism

Truncated triangular prism
(3D model)
Rank	3
Elements
Faces	2 ditrigons, 3 rectangular-symmetric octagons, 6 isosceles triangles
Edges	3+6+6+12
Vertices	6+12
Vertex figures	6 isosceles triangles
	12 scalene triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Triakis triangular tegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	A2×A1, order 12
Convex	Yes
Nature	Tame

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

Vertex coordinates

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

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

Related polytopes

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