Compound of six pentagrammic antiprisms

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Compound of six pentagrammic antiprisms
Rank3
TypeUniform
Notation
Bowers style acronymSassid
Elements
Components6 pentagrammic antiprisms
Faces60 triangles, 12 pentagrams
Edges60+60
Vertices60
Vertex figureIsosceles trapezoid, edge length 1, 1, 1, (5–1)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles5/2–3:
 3–3:
Central density12
Number of external pieces360
Level of complexity66
Related polytopes
ArmyNon-uniform Snid
RegimentSassid
DualCompound of six pentagrammic antitegums
ConjugateCompound of six pentagrammic antiprisms
Convex coreNon-Catalan pentagonal hexecontahedron
Abstract & topological properties
Flag count480
OrientableYes
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame


The small snub dodecahedron, sassid, or compound of six pentagrammic antiprisms is a uniform polyhedron compound. It consists of 60 triangles and 12 pentagrams, with one pentagram and three triangles joining at a vertex.

Its quotient prismatic equivalent is the pentagrammic antiprismatic hexateroorthowedge, which is eight-dimensional.

Vertex coordinates[edit | edit source]

The vertices of a small snub dodecahedron of edge length 1 are given by all even permutations and even sign changes of:

Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the small disnub dodecahedron.

External links[edit | edit source]