Pentagonal-pentagrammic duoprism

The pentagonal-pentagrammic duoprism, also known as starpedip or the 5-5/2 duoprism, is a uniform duoprism that consists of 5 pentagonal prisms and 5 pentagrammic prisms, with 2 of each at each vertex.

Pentagonal-pentagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymStarpedip
Coxeter diagramx5o x5/2o ()
Elements
Cells5 pentagonal prisms, 5 pentagrammic prisms
Faces25 squares, 5 pentagons, 5 pentagrams
Edges25+25
Vertices25
Vertex figureDigonal disphenoid, edge lengths (5+1)/2 (base 1), (5–1)/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius1
Hypervolume
Dichoral anglesStip–5/2–stip: 108°
 Pip–4–stip: 90°
 Pip–5–pip: 36°
Central density2
Number of external pieces15
Level of complexity12
Related polytopes
ArmySemi-uniform pedip
RegimentStarpedip
DualPentagonal-pentagrammic duotegum
ConjugatePentagonal-pentagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2×H2, order 100
ConvexNo
NatureTame

This is the only duoprism aside from the tesseract to have a circumradius equal to its edge length. A consequence of this is that two opposite pentagonal-pentagrammic duoprisms can be vertex-inscribed into the great duoantiprism.

The pentagonal-pentagrammic duoprism can be edge-inscribed into the small stellated hecatonicosachoron. The small stellated hecatonicosachoron's regiment contains a uniform compound of 24 pentagonal-pentagrammic duoprisms.

Vertex coordinates edit

The coordinates of a pentagonal-pentagrammic duoprism, centered at the origin and with unit edge length, are given by:

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External links edit