|Bowers style acronym||Odip|
|Coxeter diagram||x8o x8o ()|
|Cells||16 octagonal prisms|
|Faces||64 squares, 16 octagons|
|Vertex figure||Tetragonal disphenoid, edge lengths √ (bases) and √ (sides)|
|Measures (edge length 1)|
|Dichoral angles||Op–8–op: 135°|
|Number of external pieces||16|
|Level of complexity||3|
|Abstract & topological properties|
|Symmetry||I2(8)≀S2, order 512|
The octagonal duoprism or odip, also known as the octagonal-octagonal duoprism, the 8 duoprism or the 8-8 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 16-7 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.
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 square-square prismantiprismoid, which is also nonuniform.
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 (BC2×I2(8) symmetry)
- x4x x4x (BC2×BC2 symmetry, both octagons as ditetragons)
- xwwx xxxx4xxxx&#xt (BC2×A1 axial, octagonal prism-first)
Related polychora[edit | edit source]
Non-adjacent 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.
[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
- Klitzing, Richard. "odip".
- Wikipedia Contributors. "8-8 duoprism".