Triangular duocomb

Triangular duocomb
Rank	3
Type	Regular
Space	Spherical, 4-dimensional
Notation
Schläfli symbol	$\{4,4\mid3\}$ $\{4,4\}_6$
Elements
Faces	9 squares
Edges	18
Vertices	9
Vertex figure	Skew square, edge length √2, length 1 between opposite vertices
Petrie polygons	6 skew hexagons
Measures (edge length 1)
Surface area	9
Related polytopes
Army	Triddip
Regiment	Triddip
Dual	Triangular duocomb
Abstract properties
Euler characteristic	0
Schläfli type	{4,4}
Topological properties
Surface	Torus
Orientable	Yes
Genus	1
Properties
Symmetry	A2≀S2, order 72

The triangular duocomb is a regular skew polyhedron found within four-dimensional Euclidean space. It can be formed as the comb product of two triangles, or the modified Schläfli symbol $\{4,4\mid3\}$. It has 9 square faces, 18 edges, and 9 vertices. It is a self-dual polyhedron.

Vertex coordinates

The triangular duocomb shares its vertices and edges with the triangular duoprism, so its coordinates are

• $\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),$
• $\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$
• $\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),$
• $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right).$

External links

Wikipedia Contributors. Regular skew polyhedron

Klitzing, Richard. Skew polytopes

Klitzing, Richard. Regular maps