Square duocomb

Square duocomb
(OFF file)
Rank	3
Type	Regular
Space	Spherical, 4-dimensional
Notation
Schläfli symbol	$\{4,4\mid 4\}$
Elements
Faces	16 squares
Edges	32
Vertices	16
Vertex figure	Skew square, edge length √2, length √2 between opposite vertices
Petrie polygons	8 skew octagons
Measures (edge length 1)
Surface area	16
Related polytopes
Army	Tes
Regiment	Tes
Dual	Square duocomb
Abstract properties
Flag count	128
Euler characteristic	0
Schläfli type	{4,4}
Topological properties
Surface	Flat torus
Orientable	Yes
Genus	1

The square duocomb is a regular skew polyhedron found within four-dimensional Euclidean space. It can be formed as the comb product of two squares, or the from the extended Schläfli symbol $\{4,4\mid 4\}$. It has 16 square faces, 32 edges, and 16 vertices. It is a self-dual polyhedron.

Vertex coordinates

The square duocomb shares its vertices and edges with the tesseract, so its coordinates are

• $\left(\pm\frac{1}{2},\pm\frac{1}{2},\pm\frac{1}{2},\pm\frac{1}{2}\right)$

Related polytopes

The square duocomb appears as the facet of the petrial tesseract, which is a regular skew polychoron.

External links

• Wikipedia Contributors. "Regular skew polyhedron".
• Klitzing, Richard. Skew polytopes
• Hartley, Michael. "{4,4}*128".