Square-enneagonal duoprism

From Polytope Wiki
Jump to navigation Jump to search
Square-enneagonal duoprism
4-9 duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymSendip
Info
Coxeter diagramx4o x9o
SymmetryBC2×I2(9), order 144
ArmySendip
RegimentSendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/9) (base 1) and 2 (base 2 and sides)
Cells9 cubes, 4 enneagonal prisms
Faces9+36 squares, 4 enneagons
Edges36+36
Vertices36
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesCube–4–cube: 140°
 Cube–4–ep: 90°
 Ep–9–ep: 90°
Height1
Central density1
Euler characteristic0
Number of pieces13
Level of complexity6
Related polytopes
DualSquare-enneagonal duotegum
ConjugatesSquare-enneagrammic duoprism, Square-great enneagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The square-enneagonal duoprism or sendip, also known as the 4-9 duoprism, is a uniform duoprism that consists of 4 enneagonal prisms and 9 cubes, with two of each joining at each vertex. It is also a convex segmentochoron, being the prism of the enneagonal prism.

Vertex coordinates[edit | edit source]

The coordinates of a square-enneagonal duoprism, centered at the origin and with edge length 2sin(π/9), are given by:

  • (±sin(π/9), ±sin(π/9), 1, 0),
  • (±sin(π/9), ±sin(π/9), cos(2π/9), ±sin(2π/9)),
  • (±sin(π/9), ±sin(π/9), cos(4π/9), ±sin(4π/9)),
  • (±sin(π/9), ±sin(π/9), –1/2, ±3/2),
  • (±sin(π/9), ±sin(π/9), cos(8π/9), ±sin(8π/9)).

Representations[edit | edit source]

A square-enneagonal duoprism has the following Coxeter diagrams:

  • x4o x9o (full symmetry)
  • x x x9o (squares as rectangles)

External links[edit | edit source]