Decagrammic prism

Decagrammic prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Stiddip
Coxeter diagram	x x10/3o ()
Elements
Faces	10 squares, 2 decagrams
Edges	10+20
Vertices	20
Vertex figure	Isosceles triangle, edge lengths √2, √2, √(5–√5)/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{7-2\sqrt5}}{2} ≈ 0.79496$
Volume	$\frac{5\sqrt{5-2\sqrt5}}{2} ≈ 1.81636$
Dihedral angles	4–10/3: 90°
	4–4: 72°
Height	1
Central density	3
Number of pieces	22
Level of complexity	6
Related polytopes
Army	Semi-uniform Dip
Regiment	Stiddip
Dual	Decagrammic tegum
Conjugate	Decagonal prism
Convex core	Decagonal prism
Abstract properties
Euler characteristic	2
Topological properties
Orientable	Yes
Properties
Symmetry	I2(10)×A1, order 40
Convex	No
Nature	Tame

The decagrammic prism, or stiddip, is a prismatic uniform polyhedron. It consists of 2 decagrams and 10 squares. Each vertex joins one decagram and two squares. As the name suggests, it is a prism based on a decagram.

Vertex coordinates

A decagrammic prism of edge length 1 has vertex coordinates given by:

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

Representations

A decagrammic prism has the following Coxeter diagrams:

• x x10/3o (full symmetry)
• x x5/3x (base with H2 symmetry)

Related polyhedra

The great rhombisnub dodecahedron is a uniform polyhedron compound composed of 6 decagrammic prisms.

External links

• Klitzing, Richard. "stiddip".

• Wikipedia Contributors. "Decagrammic prism".