# Triangular duocomb

Triangular duocomb
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol{4,4∣3}
${\displaystyle \{4,4\}_{6}}$
Elements
Faces9 squares
Edges18
Vertices9
Vertex figureSkew square, edge length 2, length 1 between opposite vertices
Petrie polygons6 hexagonal-triangular coils
${\displaystyle \left\{{\dfrac {6}{1,2}}\right\}}$
Measures (edge length 1)
Surface area9
Dihedral angle${\displaystyle 60^{\circ }}$
Related polytopes
ArmyTriddip
RegimentTriddip
DualTriangular duocomb
Petrie dualPetrial triangular duocomb
HalvingHalved triangular duocomb
Abstract & topological properties
Flag count72
Euler characteristic0
Schläfli type{4,4}
SurfaceFlat torus
OrientableYes
Genus1
Properties
SymmetryA2≀S2, order 72
Dimension vector(3,2,3)

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∣3}. 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

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

## Related polytopes

The triangular duocomb can be halved or holoalternated to become the halved triangular duocomb.