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In geometry, the small icosihemidodecahedron is a uniform star polyhedron, indexed as U49. Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral.
It is given a Wythoff symbol, 3/2 3 | 5, but that construction represents a double covering of this model.
It is a hemipolyhedron with its six decagonal faces passing through the model center.
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).
References
Small icosihemidodecahedron Wikipedia(Text) CC BY-SA