# Square-enneagonal duoprism

(Redirected from Sendip)
Square-enneagonal duoprism
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${\displaystyle \frac{\sqrt{2+\frac{1}{\sin^2\frac\pi9}}}{2} ≈ 1.62393}$
Hypervolume${\displaystyle \frac{9}{4\tan\frac\pi9} ≈ 6.18182}$
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

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

A square-enneagonal duoprism has the following Coxeter diagrams:

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