|Bowers style acronym||Gidhid|
|Faces||12 pentagrams, 6 decagrams|
|Vertex figure||Bowtie, edge lengths (√5–1)/2 and √(5–√5)/2 |
|Measures (edge length 1)|
|Number of external pieces||420|
|Level of complexity||22|
|Army||Id, edge length|
|Abstract & topological properties|
|Symmetry||H3, order 120|
The great dodecahemidodecahedron, or gidhid, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagrams and 6 "hemi" decagrams, with two of each joining at a vertex. Its pentagrammic faces, as well as its hemi decagrammic faces, are parallel to those of a dodecahedron: hence the name "dodecahemidodecahedron". The "great" suffix, used for stellations in general, distinguishes it from the small dodecahemidodecahedron, which also has this face arrangement. It can be derived as a rectified petrial great icosahedron.
It is a faceting of the great icosidodecahedron, keeping the original's pentagrams while also using its equatorial decagrams.
It is notable as the only non-regular uniform polyhedron to use exclusively star polygons as faces.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the great icosidodecahedron.
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#31).
- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#3 under gid).
- Klitzing, Richard. "gidhid".
- Wikipedia Contributors. "Great dodecahemidodecahedron".
- McCooey, David. "Great dodecahemidodecahedron"