Pentagrammic-decagrammic duoprism

Pentagrammic-decagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stastidedip
Coxeter diagram	x5/2o x10/3o ()
Elements
Cells	10 pentagrammic prisms, 5 decagrammic prisms
Faces	50 squares, 10 pentagrams, 5 decagrams
Edges	50+50
Vertices	50
Vertex figure	Digonal disphenoid, edge lengths (√5–1)/2 (base 1), √(5–√5)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {10-3{\sqrt {5}}}{5}}}\approx 0.81139$
Hypervolume	$25{\frac {{\sqrt {5}}-2}{8}}\approx 0.73771$
Dichoral angles	Stip–4–stiddip: 90°
	Stip–5/2–stip: 72°
	Stiddip–10/3–stiddip: 36°
Central density	6
Number of external pieces	30
Level of complexity	24
Related polytopes
Army	Semi-uniform padedip
Regiment	Stastidedip
Dual	Pentagrammic-decagrammic duotegum
Conjugate	Pentagonal-decagonal duoprism
Abstract & topological properties
Flag count	1200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×I2(10), order 200
Convex	No
Nature	Tame

The pentagrammic-decagrammic duoprism, also known as stastidedip or the 5/2-10/3 duoprism, is a uniform duoprism that consists of 10 pentagrammic prisms and 5 decagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

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

• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$,
• $\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$,
• $\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$,
• $\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$.

Representations

A pentagrammic-decagrammic duoprism duoprism has the following Coxeter diagrams:

• x5/2o x10/3o () (full symmetry)
• x5/2o x5/3x () (H₂×H₂ symmetry, decagons as dipentagons)

External links

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

• Klitzing, Richard. "stastidedip".