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Uniform polyhedra and duals
Polyhedra {{Polyhedron-stub
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as . It has 26 faces (20 triangles
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensiona ...
and 6 decagons), 60 edges, and 30 vertices. Its vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a general -polytope is sliced off.
Definitions
Take some corner or Vertex (geometry), vertex of a polyhedron. Mark a point somewhere along each connected ed ...
alternates two regular triangles and decagons as a crossed quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
. 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 its six decagonal faces passing through the model center.
It is given a Wythoff symbol, but that construction represents a double covering of this model.
Related polyhedra
It shares its edge arrangement with theicosidodecahedron
In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (''icosi-'') triangular faces and twelve (''dodeca-'') pentagonal faces. An icosidodecahedron has 30 identical Vertex (geometry), vertices, with two triang ...
(its convex hull
In geometry, the convex hull, 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 triangular faces in common), and with the small dodecahemidodecahedron (having the decagonal faces in common).
See also
* Pentakis icosidodecahedron * List of uniform polyhedraReferences
External links
*Uniform polyhedra and duals
Polyhedra {{Polyhedron-stub