Enneagonal duoprism
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Enneagonal duoprism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Edip 
Coxeter diagram  x9o x9o () 
Elements  
Cells  18 enneagonal prisms 
Faces  81 squares, 18 enneagons 
Edges  162 
Vertices  81 
Vertex figure  Tetragonal disphenoid, edge lengths 2cos(π/9) (bases) and √2 (sides) 
Measures (edge length 1)  
Circumradius  
Inradius  
Hypervolume  
Dichoral angles  Ep–9–ep: 140° 
Ep–4–ep: 90°  
Central density  1 
Number of external pieces  18 
Level of complexity  3 
Related polytopes  
Army  Edip 
Regiment  Edip 
Dual  Enneagonal duotegum 
Conjugates  Enneagrammic duoprism, Great enneagrammic duoprism 
Abstract & topological properties  
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  I_{2}(9)≀S_{2}, order 648 
Convex  Yes 
Nature  Tame 
The enneagonal duoprism or edip, also known as the enneagonalenneagonal duoprism, the 9 duoprism or the 99 duoprism, is a noble uniform duoprism that consists of 18 enneagonal prisms, with 4 joining at each vertex. It is also the 188 gyrochoron. It is the first in an infinite family of isogonal enneagonal dihedral swirlchora and also the first in an infinite family of isochoric enneagonal hosohedral swirlchora.
This polychoron can be subsymmetrically faceted into a triangular triswirlprism, although it cannot be made uniform.
Gallery[edit  edit source]

Wireframe, cell, net
Vertex coordinates[edit  edit source]
The coordinates of an enneagonal duoprism, centered at the origin and with edge length 2sin(π/9), are given by:
where j, k = 2, 4, 8.
 (1, 0, 1, 0),
 (1, 0, cos(2π/9), ±sin(2π/9)),
 (1, 0, cos(4π/9), ±sin(4π/9)),
 (1, 0, –1/2, ±√3/2),
 (1, 0, cos(8π/9), ±sin(8π/9)),
 (cos(2π/9), ±sin(2π/9), 1, 0),
 (cos(2π/9), ±sin(2π/9), cos(2π/9), ±sin(2π/9)),
 (cos(2π/9), ±sin(2π/9), cos(4π/9), ±sin(4π/9)),
 (cos(2π/9), ±sin(2π/9), –1/2, ±√3/2),
 (cos(2π/9), ±sin(2π/9), cos(8π/9), ±sin(8π/9)),
 (cos(4π/9), ±sin(4π/9), 1, 0),
 (cos(4π/9), ±sin(4π/9), cos(2π/9), ±sin(2π/9)),
 (cos(4π/9), ±sin(4π/9), cos(4π/9), ±sin(4π/9)),
 (cos(4π/9), ±sin(4π/9), –1/2, ±√3/2),
 (cos(4π/9), ±sin(4π/9), cos(8π/9), ±sin(8π/9)),
 (–1/2, ±√3/2, 1, 0),
 (–1/2, ±√3/2, cos(2π/9), ±sin(2π/9)),
 (–1/2, ±√3/2, cos(4π/9), ±sin(4π/9)),
 (–1/2, ±√3/2, –1/2, ±√3/2),
 (–1/2, ±√3/2, cos(8π/9), ±sin(8π/9)),
 (cos(8π/9), ±sin(8π/9), 1, 0),
 (cos(8π/9), ±sin(8π/9), cos(2π/9), ±sin(2π/9)),
 (cos(8π/9), ±sin(8π/9), cos(4π/9), ±sin(4π/9)),
 (cos(8π/9), ±sin(8π/9), –1/2, ±√3/2),
 (cos(8π/9), ±sin(8π/9), cos(8π/9), ±sin(8π/9)).
External links[edit  edit source]
 Bowers, Jonathan. "Category A: Duoprisms".
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "nndip".