Pentagonal-octagrammic duoprism

Pentagonal-octagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pistodip
Coxeter diagram	x5o x8/3o ()
Elements
Cells	8 pentagonal prisms, 5 octagrammic prisms
Faces	40 squares, 8 pentagons, 5 octagrams
Edges	40+40
Vertices	40
Vertex figure	Digonal disphenoid, edge lengths (1+√5)/2 (base 1), √2–√2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {15-5{\sqrt {2}}+{\sqrt {5}}}{10}}}\approx 1.00822$
Hypervolume	${\frac {\sqrt {75-50{\sqrt {2}}+30{\sqrt {5}}-20{\sqrt {10}}}}{2}}\approx 8.30720$
Dichoral angles	Stop–8/3–stop: 108°
	Pip–4–stop: 90°
	Pip–5–pip: 45°
Central density	3
Number of external pieces	21
Level of complexity	12
Related polytopes
Army	Semi-uniform podip
Regiment	Pistodip
Dual	Pentagonal-octagrammic duotegum
Conjugates	Pentagonal-octagonal duoprism, Pentagrammic-octagonal duoprism, Pentagrammic-octagrammic duoprism
Abstract & topological properties
Flag count	960
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×I2(8), order 160
Convex	No
Nature	Tame

The pentagonal-octagrammic duoprism, also known as pistodip or the 5-8/3 duoprism, is a uniform duoprism that consists of 8 pentagonal prisms and 5 octagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of a pentagonal-octagrammic duoprism, centered at the origin and with edge length 1, are given by:

• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{20}}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{20}}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)$,
• $\left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)$.

Representations

A pentagonal-octagrammic duoprism has the following Coxeter diagrams:

• x5o x8/3o () (full symmetry)
• x4/3x x5o () (B₂×H₂ symmetry, octagrams as ditetragrams)

External links

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

• Klitzing, Richard. "pistodip".