# Triangular duocomb

Triangular duocomb
Rank3
TypeRegular
SpaceSpherical, 4-dimensional
Notation
Schläfli symbol${\displaystyle \{4,4\mid3\}}$
${\displaystyle \{4,4\}_6}$
Elements
Faces9 squares
Edges18
Vertices9
Vertex figureSkew square, edge length 2, length 1 between opposite vertices
Petrie polygons6 skew hexagons
Measures (edge length 1)
Surface area9
Related polytopes
ArmyTriddip
RegimentTriddip
DualTriangular duocomb
Abstract properties
Euler characteristic0
Schläfli type{4,4}
Topological properties
SurfaceTorus
OrientableYes
Genus1
Properties
SymmetryA2≀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 ${\displaystyle \{4,4\mid3\}}$. 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

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