In geometry, the great icosihemidodecahedron (or great icosahemidodecahedron) is a nonconvex uniform polyhedron, indexed as U₇₁. It has 26 faces (20 triangles and 6 decagrams), 60 edges, and 30 vertices.^[1] Its vertex figure is a crossed quadrilateral.

Great icosihemidodecahedron
Type	Uniform star polyhedron
Elements	F = 26, E = 60 V = 30 (χ = −4)
Faces by sides	20{3}+6{10/3}
Coxeter diagram
Wythoff symbol	3/2 3 | 5/3
Symmetry group	Ih, [5,3], *532
Index references	U71, C85, W106
Dual polyhedron	Great icosihemidodecacron
Vertex figure	3.10/3.3/2.10/3
Bowers acronym	Geihid

It is a hemipolyhedron with 6 decagrammic faces passing through the model center.

Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the triangular faces in common), and with the great dodecahemidodecahedron (having the decagrammic faces in common).

Great icosidodecahedron	Great dodecahemidodecahedron	Great icosihemidodecahedron
Icosidodecahedron (convex hull)

• List of uniform polyhedra