Octagonal duoprism
Octagonal duoprism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Odip 
Coxeter diagram  x8o x8o () 
Elements  
Cells  16 octagonal prisms 
Faces  64 squares, 16 octagons 
Edges  128 
Vertices  64 
Vertex figure  Tetragonal disphenoid, edge lengths √2+√2 (bases) and √2 (sides) 
Measures (edge length 1)  
Circumradius  
Inradius  
Hypervolume  
Dichoral angles  Op–8–op: 135° 
Op–4–op: 90°  
Central density  1 
Number of external pieces  16 
Level of complexity  3 
Related polytopes  
Army  Odip 
Regiment  Odip 
Dual  Octagonal duotegum 
Conjugate  Octagrammic duoprism 
Abstract & topological properties  
Flag count  1536 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  I_{2}(8)≀S_{2}, order 512 
Flag orbits  3 
Convex  Yes 
Nature  Tame 
The octagonal duoprism or odip, also known as the octagonaloctagonal duoprism, the 8 duoprism or the 88 duoprism, is a noble uniform duoprism that consists of 16 octagonal prisms, with 4 joining at each vertex. It is also the digonal double gyrotrapezohedroid and the 167 gyrochoron. It is the first in an infinite family of isogonal octagonal dihedral swirlchora, the first in an infinite family of isochoric octagonal hosohedral swirlchora and also the first in an infinite family of isochoric digonal tegmatic swirlchora.
The octagonal duoprism can be vertexinscribed into a small rhombated tesseract or small prismatotetracontoctachoron.
This polychoron can be alternated into a square duoantiprism, although it cannot be made uniform. Eight of the octagons can also be alternated into long rectangles to create a squaresquare prismantiprismoid, which is also nonuniform.
It can form a nonWythoffian uniform hyperbolic tiling with 288 octagonal duoprisms at each vertex with a bitetracontoctachoron as the vertex figure, called an octagonal duoprismatic tetracomb.
Gallery[edit  edit source]

Wireframe, cell, net
Vertex coordinates[edit  edit source]
Coordinates for the vertices of an octagonal duoprism of edge length 1, centered at the origin, are given by:
 ,
 ,
 ,
 .
Representations[edit  edit source]
An octagonal duoprism has the following Coxeter diagrams:
 x8o x8o () (full symmetry)
 x4x x8o () (B_{2}×I_{2}(8) symmetry)
 x4x x4x () (B_{2}×B_{2} symmetry, both octagons as ditetragons)
 xwwx xxxx4xxxx&#xt (B_{2}×A_{1} axial, octagonal prismfirst)
Related polytopes[edit  edit source]
Nonadjacent cells of the octagonal duoprism can be augmented with square pucofastegiums. If 8 cells are augmented in this way, so that all the cupolas blend with the prisms into small rhombicuboctahedra, the result is the uniform small rhombated tesseract.
An octagonal duoprism of edge length 1 contains the vertices of a hexadecachoron of edge length , since the hexadecachoron is the 83 step prism.
External links[edit  edit source]
 Bowers, Jonathan. "Category A: Duoprisms".
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "odip".
 Wikipedia contributors. "Duoprism".