In geometry, the pentakis icosidodecahedron or subdivided icosahedron is a convex polyhedron with 80 triangular faces, 120 edges, and 42 vertices.

Its name comes from a topological construction from the icosidodecahedron with the kis operator applied to the pentagonal faces.

It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices.

Buckminster Fuller referred to it as the 2-frequency alternate geodesic subdivision of the icosahedron, because the edges are divided into 2 equal parts and then lengthed slightly to keep the new vertices on a geodesic great circle, creating a polyhedron with two distinct edge lengths and face shapes.

It represents the exterior envelope of a vertex-centered orthogonal projection of the 600-cell, one of six convex regular 4-polytopes, into 3 dimensions.