Octagrammic-decagrammic duoprism

Octagrammic-decagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stostidedip
Coxeter diagram	x8/3o x10/3o ()
Elements
Cells	10 octagrammic prisms, 8 decagrammic prisms
Faces	80 squares, 10 octagrams, 8 decagrams
Edges	80+80
Vertices	80
Vertex figure	Digonal disphenoid, edge lengths √2–√2 (base 1), √(5–√5)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5-{\sqrt {2}}-{\sqrt {5}}}{2}}}\approx 0.82150$
Hypervolume	$5{\sqrt {15-10{\sqrt {2}}-6{\sqrt {5}}+4{\sqrt {10}}}}\approx 1.50472$
Dichoral angles	Stop–4–stiddip: 90°
	Stop–8/3–stop: 72°
	Stiddip–10/3–stiddip: 45°
Central density	9
Number of external pieces	36
Level of complexity	24
Related polytopes
Army	Semi-uniform odedip
Regiment	Stostidedip
Dual	Octagrammic-decagrammic duotegum
Conjugates	Octagonal-decagonal duoprism, Octagonal-decagrammic duoprism, Octagrammic-decagonal duoprism
Abstract & topological properties
Flag count	1920
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(10), order 320
Convex	No
Nature	Tame

The octagrammic-decagrammic duoprism, also known as stostidedip or the 8/3-10/3 duoprism, is a uniform duoprism that consists of 10 octagrammic prisms and 8 decagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

The vertex coordinates of an octagrammic-decagrammic duoprism, centered at the origin and with unit edge length, are given by:

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

Representations

An octagrammic-decagrammic duoprism has the following Coxeter diagrams:

• x8/3o x10/3o () (full symmetry)
• x4/3x x10/3o () (B₂×I₂(10) symmetry, octagons as ditetragons)
• x5/3x x8/3o () (H₂×I₂(8) symmetry, decagrams as distellagrams)
• x4/3x x5/3x () (B₂×H₂ symmetry)

External links

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

• Klitzing, Richard. "nd-mb-dip".