Small icosicosidodecahedral alterprism

Small icosicosidodecahedral alterprism
Rank	4
Type	Scaliform
Space	Spherical
Notation
Bowers style acronym	Siida (also Siidcup)
Coxeter diagram
Elements
Cells	2 small icosicosidodecahedra, 12 pentagrammic antiprisms, 40 triangular cupolae
Faces	40+120 triangles, 60 squares, 24 pentagrams, 40 hexagons
Edges	120+120+120
Vertices	120
Vertex figure	Skewed wedge
Measures (edge length 1)
Circumradius	$\sqrt{\frac{4+\sqrt5}2} ≈ 1.76580$
Height	$\sqrt{\frac{\sqrt5-1}2} ≈ 0.786151$
Number of external pieces	174
Related polytopes
Army	Semi-uniform sriddip
Regiment	Siidcup
Conjugate	No real conjugate
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small icosicosidodecahedral alterprism, small icosicosidodecahedral cupoliprism, or siidcup, is a scaliform polychoron. It consists of two small icosicosidodecahedra as bases, joined by 12 pentagrammic antiprisms and 40 triangular cupolae. 1 small icosicosidodecahedron, 1 pentagrammic antiprism, and 3 triangular cupolae join at each vertex. It can be formed by alternated faceting of the rhombicosidodecahedral prism. It can also be formed by partial Stott expansion of the small ditrigonary icosidodecahedral alterprism, expanding to .

It is also a segmentochoron, as siid atop siid.

External links

• Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S3).

• Klitzing, Richard. "siidcup".