Octagonal-decagonal duoprism

Octagonal-decagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Odedip
Coxeter diagram	x8o x10o ()
Elements
Cells	10 octagonal prisms, 8 decagonal prisms
Faces	80 squares, 10 octagons, 8 decagons
Edges	80+80
Vertices	80
Vertex figure	Digonal disphenoid, edge lengths √2+√2 (base 1), √(5+√5)/2 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {2}}+{\sqrt {5}}}{2}}}\approx 2.07970$
Hypervolume	$5{\sqrt {15+10{\sqrt {2}}+6{\sqrt {5}}+4{\sqrt {10}}}}\approx 37.15093$
Dichoral angles	Op–8–op: 144°
	Dip–10–dip: 135°
	Dip–4–op: 90°
Central density	1
Number of external pieces	18
Level of complexity	6
Related polytopes
Army	Odedip
Regiment	Odedip
Dual	Octagonal-decagonal duotegum
Conjugates	Octagonal-decagrammic duoprism, Octagrammic-decagonal duoprism, Octagrammic-decagrammic duoprism
Abstract & topological properties
Flag count	1920
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(10), order 320
Flag orbits	6
Convex	Yes
Nature	Tame

The octagonal-decagonal duoprism or odedip, also known as the 8-10 duoprism, is a uniform duoprism that consists of 8 decagonal prisms and 10 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-pentagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-square prismantiprismoid, which is also nonuniform.

Gallery

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  Net

Vertex coordinates

The vertices of an octagonal-decagonal duoprism of edge length 1, centered at the origin, are given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}}\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}}\right)$.

Representations

An octagonal-decagonal duoprism has the following Coxeter diagrams:

• x8o x10o () (full symmetry)
• x4x x10o () (B₂×I₂(10) symmetry, octagons as ditetragons)
• x5x x8o () (H₂×I₂(8) symmetry, decagons as dipentagons)
• x4x x5x () (B₂×H₂ symmetry, both of these applied)

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "odedip".