Halved triangular duocomb

Halved triangular duocomb
Rank	3
Dimension	4
Type	Regular
Notation
Schläfli symbol	$\left\{{\frac {4}{1,2}},4:{\frac {6}{1,3}}\right\}$
Elements
Faces	9 skew squares
Edges	18
Vertices	9
Vertex figure	Square, edge length ${\sqrt {2}}/2$
Petrie polygons	6 skew hexagons
Holes	12 triangles
Related polytopes
Army	Triddip, edge length ${\sqrt {2}}/2$
Regiment	Triddip
Petrie dual	Petrial halved triangular duocomb
Halving	Triangular duocomb
Convex hull	Triangular duoprism
Abstract & topological properties
Flag count	72
Euler characteristic	0
Schläfli type	{4,4}
Surface	4-fold cover of a flat torus
Orientable	Yes
Genus	1
Properties
Symmetry	A2≀S2, order 72
Convex	No
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:

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

Gallery

• 

  The fundamental domain of a halved triangular duocomb, with one face highlighted in orange.

External links

• Hartley, Michael. "{4,4}*72".
• Wedd, N. {4,4}_(3,0)