# Square duocomb

Square duocomb
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol{4,4∣4}
Elements
Faces16 squares
Edges32
Vertices16
Vertex figureSkew square, edge length 2, length 2 between opposite vertices
Petrie polygons8 octagonal-octagrammic coils
${\displaystyle \left\{{\dfrac {8}{1,3}}\right\}}$
Holes16 squares
Measures (edge length 1)
Surface area16
Dihedral angle${\displaystyle 90^{\circ }}$
Related polytopes
ArmyTes
RegimentTes
DualSquare duocomb
Petrie dualPetrial square duocomb
HalvingHalved square duocomb
Abstract & topological properties
Flag count128
Euler characteristic0
Schläfli type{4,4}
SurfaceFlat torus
OrientableYes
Genus1
Properties
Flag orbits1
ConvexNo
Dimension vector(3,2,3)

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∣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.