Snub dodecahedral prism
The snub dodecahedral prism or sniddip is a prismatic uniform polychoron that consists of 2 snub dodecahedra, 12 pentagonal prisms, and 20+60 triangular prisms. Each vertex joins 1 snub dodecahedron, 1 pentagonal prism, and 4 triangular prisms. It is a prism based on the snub dodecahedron. As such it is also a convex segmentochoron (designated K-4.110 on Richard Klitzing's list).
|Snub dodecahedral prism|
|Bowers style acronym||Sniddip|
|Coxeter diagram||x2s5s3s ()|
|Cells||20+60 triangular prisms, 12 pentagonal prisms, 2 snub dodecahedra|
|Faces||40+120 triangles, 30+60+60 squares, 24 pentagons|
|Vertex figure||Mirror-symmetric (topologically irregular) pentagonal pyramid, edge lengths 1, 1, 1, 1, (1+√5)/2 (base), √2 (legs)|
|Measures (edge length 1)|
|Dichoral angles||Trip–4–trip: ≈ 164.17537°|
|Trip–4–pip: ≈ 152.92992°|
|Number of external pieces||94|
|Level of complexity||20|
|Dual||Pentagonal hexecontahedral tegum|
|Conjugates||Great snub icosidodecahedral prism, great inverted snub icosidodecahedral prism, great inverted retrosnub icosidodecahedral prism|
|Abstract & topological properties|
|Symmetry||H3+×A1, order 120|
The coordinates of a snub dodecahedral prism, centered at the origin and with unit edge length, are given by all even permutations with an odd number of sign changes of the first three coordinates of:
as well as all even permutations with an even number of sign changes of the first three coordinates of:
- Bowers, Jonathan. "Category 19: Prisms" (#952).
- Klitzing, Richard. "Sniddip".
- Wikipedia Contributors. "Snub dodecahedral prism".