Decagrammic duoprism

Decagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Stadidip
Coxeter diagram	x10/3o x10/3o ()
Elements
Cells	20 decagrammic prisms
Faces	100 squares, 20 decagrams
Edges	200
Vertices	100
Vertex figure	Tetragonal disphenoid, edge lengths √(5–√5)/2 (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403$
Inradius	$\frac{\sqrt{5-2\sqrt5}}{2} ≈ 0.36327$
Hypervolume	$25\frac{5-2\sqrt5}{4} ≈ 3.29915$
Dichoral angles	Stiddip–4–stiddip: 90°
	Stiddip–10/3–stiddip: 72°
Central density	9
Number of external pieces	40
Level of complexity	12
Related polytopes
Army	Dedip
Regiment	Stadidip
Dual	Decagrammic duotegum
Conjugate	Decagonal duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)≀S2, order 800
Convex	No
Nature	Tame

The decagrammic duoprism or stadidip, also known as the decagrammic-decagrammic duoprism, the 10/3 duoprism or the 10/3-10/3 duoprism, is a noble uniform duoprism that consists of 20 decagrammic prisms, with 4 meeting at each vertex.

A unit decagrammic duoprism can be vertex-inscribed into a grand ditetrahedronary hexacosidishecatonicosachoron.

Vertex coordinates

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

• $\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2}\right),$
• $\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2},\,±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}}\right),$
• $\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2},\,±\frac{\sqrt5-1}{2},\,0\right),$
• $\left(±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}},\,±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2}\right),$
• $\left(±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}},\,±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}}\right),$
• $\left(±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}},\,±\frac{\sqrt5-1}{2},\,0\right),$
• $\left(±\frac{\sqrt5-1}{2},\,0,\,±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2}\right),$
• $\left(±\frac{\sqrt5-1}{2},\,0,\,±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}}\right),$
• $\left(±\frac{\sqrt5-1}{2},\,0,\,±\frac{\sqrt5-1}{2},\,0\right).$

External links

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

• Klitzing, Richard. "stadidip".