Small icosihemidodecahedron

{{short description|Uniform star polyhedron with 26 faces}}

{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}}

File:Small icosihemidodecahedron.stl

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as {{math|U{{sub|49}}}}. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/49.html|title=49: small icosihemidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} 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, {{math|{{frac|3|2}} 3 {{!}} 5,}} but that construction represents a double covering of this model.