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Triakis icosahedron
Type	Catalan
Face polygon	isosceles triangle
Faces	60
Edges	90
Vertices	32 = 12 + 20
Face configuration	V3.10.10
Symmetry group	icosahedral (Ih)
Dual polyhedron	truncated dodecahedron
Properties	convex, face-uniform

A triakis icosahedron is a polyhedron obtained by augmenting each of the 20 triangular faces of an icosahedron with a pyramid, forming 60 isosceles triangles in all. The term is most commonly applied to one of the Catalan solids, the dual to the truncated dodecahedron.

See Triakis triangular tiling for other "triakis" polyhedral forms.

Magnus Wenninger in the book Polyhedron Models calls the first stellation of the icosahedron by this same name (Model W₂₆). Its surface topology a similarly connected 60 isosceles triangle faces, but the triangles are taller, making it concave.

Catalan solids

三方二十面体 | icosaedro triakis | Icosaedro triakis