# Snub dodecahedral antiprism

Snub dodecahedral antiprism
File:Snub dodecahedral antiprism.png
Rank4
TypeIsogonal
Notation
Bowers style acronymSniddap
Coxeter diagrams2s5s3s ()
Elements
Cells120 irregular tetrahedra, 30 rhombic disphenoids, 20 triangular gyroprisms, 12 pentagonal gyroprisms, 2 snub dodecahedra
Faces120+120+120+120 scalene triangles, 40 triangles, 24 pentagons
Edges60+60+60+60+120+120
Vertices120
Vertex figureTriangular-pentagonal gyrowedge
Measures (as derived from unit-edge great rhombicosidodecahedral prism)
Edge lengthsDiagonals of original squares (60+60+60+60): ${\displaystyle {\sqrt {2}}\approx 1.41421}$
Edges of equilateral triangles (120): ${\displaystyle {\sqrt {3}}\approx 1.73205}$
Edges of pentagons (120): ${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{2}}}\approx 1.90211}$
Circumradius${\displaystyle {\sqrt {8+3{\sqrt {5}}}}\approx 3.83513}$
Central density1
Related polytopes
ArmySniddap
RegimentSniddap
DualPentagonal hexecontahedral antitegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(H3×A1)+, order 120
ConvexYes
NatureTame

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:${\displaystyle {\frac {\sqrt {58-2{\sqrt {5}}+2{\sqrt {110+38{\sqrt {5}}}}}}{8}}\approx 1:1.12815}$.