Hexagonal-grand hendecagrammic duoprism

From Polytope Wiki
(Redirected from 6-11/5 duoprism)
Jump to navigation Jump to search
Hexagonal-grand hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx6o x11/5o
SymmetryG2×I2(11), order 264
ArmySemi-uniform hahendip
Elements
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), 2cos(5π/11) (base 2), 2 (sides)
Cells11 hexagonal prisms, 6 grand hendecagrammic prisms
Faces66 squares, 11 hexagons, 6 grand hendecagrams
Edges66+66
Vertices66
Measures (edge length 1)
Circumradius4+csc2(5π/11)/2 ≈ 1.12034
Hypervolume
Dichoral anglesHip–6–hip: π/11 ≈ 16.36364°
 11/5p–11/5–11/5p: 120°
 Hip–4–11/5p: 90°
Central density5
Related polytopes
DualHexagonal-grand hendecagrammic duotegum
ConjugatesHexagonal-hendecagonal duoprism, Hexagonal-small hendecagrammic duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The hexagonal-grand hendecagrammic duoprism, also known as the 6-11/5 duoprism, is a uniform duoprism that consists of 11 hexagonal prisms and 6 grand hendecagrammic prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a hexagonal-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:

  • (±2sin(5π/11), 0, 1, 0),
  • (±2sin(5π/11), 0, cos(2π/11), ±sin(2π/11)),
  • (±2sin(5π/11), 0, cos(4π/11), ±sin(4π/11)),
  • (±2sin(5π/11), 0, cos(6π/11), ±sin(6π/11)),
  • (±2sin(5π/11), 0, cos(8π/11), ±sin(8π/11)),
  • (±2sin(5π/11), 0, cos(10π/11), ±sin(10π/11)),
  • (±sin(5π/11), ±sin(5π/11)3, 1, 0),
  • (±sin(5π/11), ±sin(5π/11)3, cos(2π/11), ±sin(2π/11)),
  • (±sin(5π/11), ±sin(5π/11)3, cos(4π/11), ±sin(4π/11)),
  • (±sin(5π/11), ±sin(5π/11)3, cos(6π/11), ±sin(6π/11)),
  • (±sin(5π/11), ±sin(5π/11)3, cos(8π/11), ±sin(8π/11)),
  • (±sin(5π/11), ±sin(5π/11)3, cos(10π/11), ±sin(10π/11)).

External links[edit | edit source]