In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron,[1] great rhombicosidodecahedron,[2][3] omnitruncated dodecahedron or omnitruncated icosahedron[4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.

Of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a sphere in which it is inscribed, very narrowly beating the snub dodecahedron (89.63%) and small rhombicosidodecahedron (89.23%), and less narrowly beating the truncated icosahedron (86.74%); it also has by far the greatest volume (206.8 cubic units) when its edge length equals 1.

Cartesian coordinates for the vertices of a truncated icosidodecahedron with edge length 2φ − 2, centered at the origin, are all the even permutations of:[5] where φ = ⁠1 + √5/2⁠ is the golden ratio.

The truncated icosidodecahedron is the convex hull of a rhombicosidodecahedron with cuboids above its 30 squares, whose height to base ratio is φ.

Within Icosahedral symmetry there are unlimited geometric variations of the truncated icosidodecahedron with isogonal faces.

[6] This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram .