Pentagonal-hendecagrammic duoprism

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Pentagonal-hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx5o x11/3o ()
Elements
Cells11 pentagonal prisms, 5 hendecagrammic prisms
Faces55 squares, 11 pentagons, 5 hendecagrams
Edges55+55
Vertices55
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(3π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesShenp–11/3–shenp: 108°
 Pip–4–shenp: 90°
 Pip–5–pip:
Central density3
Number of external pieces27
Level of complexity12
Related polytopes
ArmySemi-uniform pahendip
DualPentagonal-hendecagrammic duotegum
ConjugatesPentagonal-hendecagonal duoprism, Pentagonal-small hendecagrammic duoprism, Pentagonal-great hendecagrammic duoprism, Pentagonal-grand hendecagrammic duoprism, Pentagrammic-hendecagonal duoprism, Pentagrammic-small hendecagrammic duoprism, Pentagrammic-hendecagrammic duoprism, Pentagrammic-great hendecagrammic duoprism, Pentagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count1320
Euler characteristic0
OrientableYes
Properties
SymmetryH2×I2(11), order 220
ConvexNo
NatureTame

The pentagonal-hendecagrammic duoprism, also known as the 5-11/3 duoprism, is a uniform duoprism that consists of 11 pentagonal prisms and 5 hendecagrammic prisms, with 2 of each at each vertex.

The name can also refer to the pentagonal-small hendecagrammic duoprism, the pentagonal-great hendecagrammic duoprism, or the pentagonal-grand hendecagrammic duoprism.

Vertex coordinates[edit | edit source]

The coordinates of a pentagonal-hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,

where j = 2, 4, 6, 8, 10.

External links[edit | edit source]