# Square duocomb

Square duocomb
Rank3
TypeRegular
SpaceSpherical, 4-dimensional
Notation
Schläfli symbol${\displaystyle \{4,4\mid 4\}}$
Elements
Faces16 squares
Edges32
Vertices16
Vertex figureSkew square, edge length 2, length 2 between opposite vertices
Petrie polygons8 skew octagons
Measures (edge length 1)
Surface area16
Related polytopes
ArmyTes
RegimentTes
DualSquare duocomb
Abstract properties
Flag count128
Euler characteristic0
Schläfli type{4,4}
Topological properties
SurfaceFlat torus
OrientableYes
Genus1

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 ${\displaystyle \{4,4\mid 4\}}$. 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

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

## Related polytopes

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