Great icosihemidodecahedron

Polyhedron with 26 faces

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	I_h, [5,3], *532
Index references	U₇₁, C₈₅, W₁₀₆
Dual polyhedron	Great icosihemidodecacron
Vertex figure	3.10/3.3/2.10/3
Bowers acronym	Geihid

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.

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

Related polyhedra

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).