In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as . It has 18 faces (12

pentagons In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simpl ...

and 6 decagons), 60

edges Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed by ...

, and 30 vertices. Its vertex figure alternates two regular

pentagon In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simpl ...

s and decagons as a crossed quadrilateral. It is a

hemipolyhedron In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of some other symmetrical polyhedron, and their count is half the number of faces of that other po ...

with six decagonal faces passing through the model center.

Related polyhedra

It shares its edge arrangement with the icosidodecahedron (its

convex hull In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ...

, having the pentagonal faces in common), and with the

small icosihemidodecahedron In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as . It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices. Its vertex figure alternates two regular triang ...

(having the decagonal faces in common).

References

External links

*
Uniform polyhedra and duals
Uniform polyhedra {{Polyhedron-stub