Decagonal-decagrammic duoprism

Decagonal-decagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Distadedip
Coxeter diagram	x10o x10/3o ()
Elements
Cells	10 decagonal prisms, 10 decagrammic prisms
Faces	100 squares, 10 decagons, 10 decagrams
Edges	100+100
Vertices	100
Vertex figure	Digonal disphenoid, edge lengths √(5+√5)/2 (base 1), √(5–√5)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {3}}\approx 1.73205$
Hypervolume	${\frac {25{\sqrt {5}}}{4}}\approx 13.97542$
Dichoral angles	Stiddip–10/3–stiddip: 144°
	Dip–4–stiddip: 90°
	Dip–10–dip: 72°
Central density	3
Number of external pieces	30
Level of complexity	12
Related polytopes
Army	Semi-uniform dedip
Regiment	Distadedip
Dual	Decagonal-decagrammic duotegum
Conjugate	Decagonal-decagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)×I2(10), order 400
Convex	No
Nature	Tame

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

This polychoron can be alternated into the great duoantiprism, which can be made uniform.

Vertex coordinates

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

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

Representations

A decagonal-decagrammic duoprism has the following Coxeter diagrams:

• x10o x10/3o (full symmetry)
• x5x x10/3o () (H₂×I₂(10) symmetry, decagons as dipentagons)

External links

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

• Klitzing, Richard. "distadedip".