Small dodecahemidodecahedron

Small dodecahemidodecahedron
Small dodecahemidodecahedron.png
Type Uniform star polyhedron
Elements F = 18, E = 60
V = 30 (χ = −12)
Faces by sides 12{5}+6{10}
Wythoff symbol 5/4 5 | 5
Symmetry group Ih, [5,3], *532
Index references U51, C65, W91
Dual polyhedron Small dodecahemidodecacron
Vertex figure Small dodecahemidodecahedron vertfig.png
5.10.5/4.10
Bowers acronym Sidhid

In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U51. It has 18 faces (12 pentagons and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.

3D model of a small dodecahemidodecahedron

It is a hemipolyhedron with six decagonal faces passing through the model center.

Related polyhedraEdit

It shares its edge arrangement with the icosidodecahedron (its convex hull, having the pentagonal faces in common), and with the small icosihemidodecahedron (having the decagonal faces in common).

 
Icosidodecahedron
 
Small icosihemidodecahedron
 
Small dodecahemidodecahedron

ReferencesEdit

  1. ^ Maeder, Roman. "51: small dodecahemidodecahedron". MathConsult.

External linksEdit