In geometry, the tridiminished icosahedron is one of the Johnson solids (J_63). The name refers to one way of constructing it, by removing three pentagonal pyramids (J_2) from a regular icosahedron, which replaces three sets of five triangular faces from the icosahedron with three mutually adjacent pentagonal faces. The tridiminished icosahedron is the vertex figure of the snub 24-cell, a uniform 4-polytope (4-dimensional polytope).