In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U<sub>68</sub>. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices. It is given a Schläfli symbol and Coxeter-Dynkin diagram, .
Cartesian coordinates for the vertices of a great truncated icosidodecahedron centered at the origin are all the even permutations of
where is the golden ratio.
The great disdyakis triacontahedron (or trisdyakis icosahedron) is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron. Its faces are triangles.
The triangles have one angle of , one of and one of The dihedral angle equals Part of each triangle lies within the solid, hence is invisible in solid models.