# Hendecagrammic duoprism

(Redirected from 11/3-11/3 duoprism)
Hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/3o x11/3o
SymmetryI2(11)≀S2, order 968
ArmyHandip
Elements
Vertex figureTetragonal disphenoid, edge lengths 2cos(3π/11) (bases) and 2 (sides)
Cells22 hendecagrammic prisms
Faces22 hendecagrams, 121 squares
Edges242
Vertices121
Measures (edge length 1)
Hypervolume121/(16tan2(3π/11)) ≈ 5.67816
Dichoral angles11/3p–11/3–11/3p: 5π/11 ≈ 81.81818°
11/3p–4–11/3p: 90°
Related polytopes
DualHendecagrammic duotegum
ConjugatesHendecagonal duoprism, Small hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The hendecagrammic duoprism, also known as the hendecagrammic-hendecagrammic duoprism, the 11/3 duoprism or the 11/3-11/3 duoprism, is a noble uniform duoprism that consists of 22 hendecagrammic prisms and 121 vertices.

## Vertex coordinates

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

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