# Pentagonal duocomb

Pentagonal duocomb
Rank3
TypeRegular
SpaceSpherical, 4-dimensional
Notation
Schläfli symbol${\displaystyle \{4,4\mid 5\}}$
${\displaystyle \{4,4\}_{(5,0)}}$
Elements
Faces25 squares
Edges50
Vertices25
Petrie polygons10 decagonal-pentagonal coils
${\displaystyle \left\{\dfrac{10}{1,2}\right\}}$
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt{5}}{5}} \approx 1.20300}$
Surface area25
Dihedral angle${\displaystyle \frac{3\pi}{5} = 108^\circ}$
Related polytopes
ArmyPedip
RegimentPedip
DualPentagonal duocomb
HalvingHalved pentagonal duocomb
ConjugatePentagrammic duocomb
Abstract & topological properties
Flag count200
Euler characteristic0
Schläfli type{4,4}
SurfaceFlat torus
OrientableYes
Genus1
Properties
ConvexNo

The pentagonal duocomb is a regular skew polyhedron found within four-dimensional Euclidean space. It can be formed as the comb product of two pentagons, or the from the extended Schläfli symbol ${\displaystyle \{4,4\mid 5\}}$. It has 25 square faces, 50 edges, and 25 vertices. It is a self-dual polyhedron.

## Vertex coordinates

Its vertex coordinates are the same as those of the pentagonal duoprism.