Small icosihemidodecahedron
Small icosihemidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Seihid |
Coxeter diagram | (x3/2o3x5*a)/2 ()/2 |
Elements | |
Faces | 20 triangles, 6 decagons |
Edges | 60 |
Vertices | 30 |
Vertex figure | Bowtie, edge lengths 1 and √(5+√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Dihedral angle | |
Number of external pieces | 80 |
Level of complexity | 4 |
Related polytopes | |
Army | Id |
Regiment | Id |
Dual | Small icosihemidodecacron |
Conjugate | Great icosihemidodecahedron |
Abstract & topological properties | |
Flag count | 240 |
Euler characteristic | –4 |
Orientable | No |
Genus | 6 |
Properties | |
Symmetry | H3, order 120 |
Convex | No |
Nature | Tame |
The small icosihemidodecahedron, or seihid, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 20 equilateral triangles and 6 central decagons, with two of each joining at a vertex. Its triangular faces are parallel to those of an icosahedron, and its hemi decagonal faces are parallel to those of a dodecahedron: hence the name "icosihemidodecahedron". The "small" suffix, used for stellations in general, distinguishes it from the great icosihemidodecahedron, which also has this face arrangement. It can be derived as a rectified petrial dodecahedron.
It is a faceting of the icosidodecahedron, keeping the original's triangles while also using its equatorial decagons.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the icosidodecahedron.
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#26).
- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#2 under id).
- Klitzing, Richard. "seihid".
- Wikipedia contributors. "Small icosihemidodecahedron".
- McCooey, David. "Small Icosihemidodecahedron"