Pentagonal-hendecagonal duoprism

From Polytope Wiki
(Redirected from 11-5 duoprism)
Jump to navigation Jump to search
Pentagonal-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPahendip
Info
Coxeter diagramx5o x11o
SymmetryH2×I2(11), order 220
ArmyPahendip
RegimentPahendip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(π/11) (base 2), and 2 (sides)
Cells11 pentagonal prisms, 5 hendecagonal prisms
Faces55 squares, 11 pentagons, 5 hendecagons
Edges55+55
Vertices55
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesPip–5–pip:
 Henp–11–henp: 108°
 Pip–4–henp: 90°
Central density1
Euler characteristic0
Number of pieces16
Level of complexity6
Related polytopes
DualPentagonal-hendecagonal duotegum
ConjugatesPentagonal-small hendecagrammic duoprism, Pentagonal-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
Properties
ConvexYes
OrientableYes
NatureTame

The pentagonal-hendecagonal duoprism or pahendip, also known as the 5-11 duoprism, is a uniform duoprism that consists of 5 hendecagonal prisms and 11 pentagonal prisms, with two of each joining at each vertex.

Vertex coordinates[edit | edit source]

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

  • (±sin(π/11), –sin(π/11)(5+25)/5, 1, 0),
  • (±sin(π/11), –sin(π/11)(5+25)/5, cos(2π/11), ±sin(2π/11)),
  • (±sin(π/11), –sin(π/11)(5+25)/5, cos(4π/11), ±sin(4π/11)),
  • (±sin(π/11), –sin(π/11)(5+25)/5, cos(6π/11), ±sin(6π/11)),
  • (±sin(π/11), –sin(π/11)(5+25)/5, cos(8π/11), ±sin(8π/11)),
  • (±sin(π/11), –sin(π/11)(5+25)/5, cos(10π/11), ±sin(10π/11)),
  • (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, 1, 0),
  • (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(2π/11), ±sin(2π/11)),
  • (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(4π/11), ±sin(4π/11)),
  • (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(6π/11), ±sin(6π/11)),
  • (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(8π/11), ±sin(8π/11)),
  • (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(10π/11), ±sin(10π/11)),
  • (0, 2sin(π/11)(5+5)/10, 1, 0),
  • (0, 2sin(π/11)(5+5)/10, cos(2π/11), ±sin(2π/11)),
  • (0, 2sin(π/11)(5+5)/10, cos(4π/11), ±sin(4π/11)),
  • (0, 2sin(π/11)(5+5)/10, cos(6π/11), ±sin(6π/11)),
  • (0, 2sin(π/11)(5+5)/10, cos(8π/11), ±sin(8π/11)),
  • (0, 2sin(π/11)(5+5)/10, cos(10π/11), ±sin(10π/11)).

External links[edit | edit source]