Snub dodecahedral antiprism

Snub dodecahedral antiprism
File:Snub dodecahedral antiprism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Sniddap
Coxeter diagram	s2s5s3s (
Elements
Cells	120 irregular tetrahedra, 30 rhombic disphenoids, 20 triangular gyroprisms, 12 pentagonal gyroprisms, 2 snub dodecahedra
Faces	120+120+120+120 scalene triangles, 40 triangles, 24 pentagons
Edges	60+60+60+60+120+120
Vertices	120
Vertex figure	Triangular-pentagonal gyrowedge
Measures (as derived from unit-edge great rhombicosidodecahedral prism)
Edge lengths	Diagonals of original squares (60+60+60+60): $\sqrt2 ≈ 1.41421$
	Edges of equilateral triangles (120): $\sqrt3 ≈ 1.73205$
	Edges of pentagons (120): $\sqrt{\frac{5+\sqrt5}{2}} ≈ 1.90211$
Circumradius	$\sqrt{8+3\sqrt5} ≈ 3.83513$
Central density	1
Related polytopes
Army	Sniddap
Regiment	Sniddap
Dual	Pentagonal hexecontahedral antitegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(H3×A1)+, order 120
Convex	Yes
Nature	Tame

The snub dodecahedral antiprism, omnisnub dodecahedral antiprism, or sniddap, also known as the alternated great rhombicosidodecahedral prism, is a convex isogonal polychoron that consists of 2 snub dodecahedra, 12 pentagonal gyroprisms, 20 triangular gyroprisms, 30 rhombic disphenoids, and 120 irregular tetrahedra. 4 tetrahedra and one of each other type of cell join at each vertex. It can be obtained through the process of alternating the great rhombicosidodecahedral prism. However, it cannot be made uniform, as it generally has 6 edge lengths, which can be minimized to no fewer than 3 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{\sqrt{58-2\sqrt5+2\sqrt{110+38\sqrt5}}}{8}$ ≈ 1:1.12815.

External links

• Klitzing, Richard. "sniddap".

• Wikipedia Contributors. "Omnisnub dodecahedral antiprism".