# Halved pentagonal duocomb

Halved pentagonal duocomb Rank3
Dimension4
TypeRegular
Elements
Faces25 skew squares
Edges50
Vertices25
Vertex figureSkew square
Petrie polygons10 skew pentagons
Related polytopes
ArmyPedip
DualHalved pentagonal duocomb
Petrie dualPetrial halved pentagonal duocomb
HalvingPentagrammic duocomb
Convex hullPentagonal duocomb
Abstract & topological properties
Flag count200
Euler characteristic0
Schläfli type{4,4}
SurfaceDouble cover of the flat torus
OrientableYes
Genus1
Properties
SymmetryH2≀S2, order 200
ConvexNo
Dimension vector(2,3,2)

The halved pentagonal duocomb is a regular skew polyhedron in 4-dimensional Euclidean space. It can be constructed by halving the pentagonal duocomb, and the two are abstractly equivalent. Halving the halved pentagonal duocomb gives the pentagrammic duocomb, and if you halve the halved pentagonal duocomb three times you return to the original pentagonal duocomb.

## Vertex coordinates

Its vertex coordinates are the same as those of the pentagonal duoprism of edge length ${\sqrt {2}}/2$ . For the halved pentagonal duocomb of edge length 1 these can be given as:

• $\left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{20}}},\,0,\,{\sqrt {\frac {5+{\sqrt {5}}}{20}}}\right)$ ,
• $\left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{20}}},\,\pm {\frac {\sqrt {3+{\sqrt {5}}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{80}}}\right)$ ,
• $\left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{20}}},\,\pm {\frac {\sqrt {2}}{4}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{40}}}\right)$ ,
• $\left(\pm {\frac {\sqrt {3+{\sqrt {5}}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{80}}},\,0,\,{\sqrt {\frac {5+{\sqrt {5}}}{20}}}\right)$ ,
• $\left(\pm {\frac {\sqrt {3+{\sqrt {5}}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{80}}},\,\pm {\frac {\sqrt {3+{\sqrt {5}}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{80}}}\right)$ ,
• $\left(\pm {\frac {\sqrt {3+{\sqrt {5}}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{80}}},\,\pm {\frac {\sqrt {2}}{4}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{40}}}\right)$ ,
• $\left(\pm {\frac {\sqrt {2}}{4}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{40}}},\,0,\,{\sqrt {\frac {5+{\sqrt {5}}}{20}}}\right)$ ,
• $\left(\pm {\frac {\sqrt {2}}{4}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{40}}},\,\pm {\frac {\sqrt {3+{\sqrt {5}}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{80}}}\right)$ ,
• $\left(\pm {\frac {\sqrt {2}}{4}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{40}}},\,\pm {\frac {\sqrt {2}}{4}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{40}}}\right)$ .