Pentagrammic duoprism

Pentagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Stardip
Coxeter diagram	x5/2o x5/2o ()
Elements
Cells	10 pentagrammic prisms
Faces	25 squares, 10 pentagrams
Edges	50
Vertices	25
Vertex figure	Tetragonal disphenoid, edge lengths (√5–1)/2 (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{5}} ≈ 0.74350$
Inradius	$\sqrt{\frac{5-2\sqrt5}{20}} ≈ 0.16246$
Hypervolume	$5\frac{5-2\sqrt5}{16} ≈ 0.16496$
Dichoral angles	Stip–4–stip: 90°
	Stip–5/2-stip: 36°
Central density	4
Number of external pieces	20
Level of complexity	12
Related polytopes
Army	Pedip
Regiment	Stardip
Dual	Pentagrammic duotegum
Conjugate	Pentagonal duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2≀S2, order 200
Convex	No
Nature	Tame

The pentagrammic duoprism or stardip, also known as the pentagrammic-pentagrammic duoprism, the 5/2 duoprism or the 5/2-5/2 duoprism, is a noble uniform duoprism that consists of 10 pentagrammic prisms, with 4 meeting at each vertex.

Gallery

• 

  GeoGebra render

Vertex coordinates

The coordinates of a pentagrammic duoprism of edge length 1, centered at the origin, are given by:

• $\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$
• $\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$
• $\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right),$
• $\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$
• $\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$
• $\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right).$

External links

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

• Klitzing, Richard. "stardip".