Small icosihemidodecahedron

Small icosihemidodecahedron

Type	Uniform star polyhedron
Elements	F = 26, E = 60 V = 30 (χ = −4)
Faces by sides	20{3}+6{10}
Coxeter diagram	(double covering)
Wythoff symbol	3/2 3 \| 5 (double covering)
Symmetry group	I_h, [5,3], *532
Index references	U₄₉, C₆₃, W₈₉
Dual polyhedron	Small icosihemidodecacron
Vertex figure	3.10.3/2.10
Bowers acronym	Seihid

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as $U 49$ . It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.^[1] Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral. It is a hemipolyhedron with its six decagonal faces passing through the model center.

It is given a Wythoff symbol, $.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}3⁄2 3 | 5,$ but that construction represents a double covering of this model.

Related polyhedra

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