Small dodecahemicosahedron
(Redirected from Sidhei)
Jump to navigation
Jump to search
| Small dodecahemicosahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Sidhei |
| Coxeter diagram | (    )/2 (x5/3o5/2x3*a)/2 |
| Elements | |
| Faces | 12 pentagrams, 10 hexagons |
| Edges | 60 |
| Vertices | 30 |
| Vertex figure | Bowtie, edge lengths (√5–1)/2 and √3  |
| Measures (edge length 1) | |
| Circumradius | 1 |
| Dihedral angle | |
| Number of pieces | 240 |
| Level of complexity | 12 |
| Related polytopes | |
| Army | Id |
| Regiment | Did |
| Dual | Small dodecahemicosacron |
| Conjugate | Great dodecahemicosahedron |
| Abstract properties | |
| Euler characteristic | –8 |
| Topological properties | |
| Orientable | No |
| Genus | 10 |
| Properties | |
| Symmetry | H3, order 120 |
| Convex | No |
| Nature | Tame |
The small dodecahemicosahedron, or sidhei, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagrams and 10 "hemi" hexagons, with two of each joining at a vertex. Its pentagrammic faces are parallel to those of a dodecahedron, and its hemi hexagonal faces are parallel to those of an icosahedron: hence the name "dodecahemicosahedron". The "small" suffix, used for stellations in general, distinguishes it from the great dodecahemicosahedron, which also has this face arrangement.
It is a faceting of the dodecadodecahedron, keeping the original's pentagrams while also using its equatorial hexagons.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the dodecadodecahedron.
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#28).
- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#2 under did).
- Klitzing, Richard. "sidhei".
- Wikipedia Contributors. "Small dodecahemicosahedron".
- McCooey, David. "Small Dodecahemicosahedron"