Small dodecahemicosahedron
Small dodecahemicosahedron  

Rank  3 
Type  Uniform 
Notation  
Bowers style acronym  Sidhei 
Coxeter diagram  ()/2 (x5/3o5/2x3*a)/2 
Elements  
Faces 

Edges  60 
Vertices  30 
Vertex figure  Bowtie, edge lengths (√5–1)/2 and √3 
Measures (edge length 1)  
Circumradius  1 
Dihedral angle  
Number of external pieces  240 
Level of complexity  12 
Related polytopes  
Army  Id, edge length 
Regiment  Did 
Dual  Small dodecahemicosacron 
Conjugate  Great dodecahemicosahedron 
Abstract & topological properties  
Flag count  240 
Euler characteristic  –8 
Orientable  No 
Genus  10 
Properties  
Symmetry  H_{3}, order 120 
Flag orbits  2 
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.
It can be derived as a rectified Petrial great dodecahedron.
It is a faceting of the dodecadodecahedron, keeping the original's pentagrams while also using its equatorial hexagons.
Name[edit  edit source]
Its pentagrammic faces are parallel to those of a dodecahedron, and its hexagonal faces are parallel to those of an icosahedron, hence the name "dodecahemicosahedron". The "small" modifier, used for stellations in general, distinguishes it from the great dodecahemicosahedron, which also has this face arrangement.
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"