# Halved triangular duocomb

Halved triangular duocomb
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol${\displaystyle \left\{{\frac {4}{1,2}},4:{\frac {6}{1,3}}\right\}}$
Elements
Faces9 skew squares
Edges18
Vertices9
Vertex figureSquare, edge length ${\displaystyle {\sqrt {2}}/2}$
Petrie polygons6 skew hexagons
Holes12 triangles
Related polytopes
ArmyTriddip, edge length ${\displaystyle {\sqrt {2}}/2}$
RegimentTriddip
Petrie dualPetrial halved triangular duocomb
HalvingTriangular duocomb
Convex hullTriangular duoprism
Abstract & topological properties
Flag count72
Euler characteristic0
Schläfli type{4,4}
Surface4-fold cover of a flat torus
OrientableYes
Genus1
Properties
SymmetryA2≀S2, order 72
ConvexNo
Dimension vector(2,3,2)

The halved triangular duocomb is a regular skew polyhedron in 4-dimensional Euclidean space. It can be constructed by halving the triangular duocomb, and the two are abstractly equivalent. Halving the halved triangular duocomb again gives the original triangular duocomb.

## Vertex coordinates

The halved triangular duocomb shares its vertices with the triangular duoprism, so its coordinates can be given as:

• ${\displaystyle \left(0,\,{\frac {\sqrt {6}}{6}},\,0,\,{\frac {\sqrt {6}}{6}}\right)}$,
• ${\displaystyle \left(0,\,{\frac {\sqrt {6}}{6}},\,\pm {\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}}\right)}$,
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}},\,0,\,{\frac {\sqrt {6}}{6}}\right)}$,
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}},\,\pm {\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}}\right)}$.