Triakis icosahedron

In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron. It has also been called the kisicosahedron.[1] It was first depicted, in a non-convex form with equilateral triangle faces, by Leonardo da Vinci in Luca Pacioli's Divina proportione, where it was named the icosahedron elevatum.[2] The capsid of the Hepatitis A virus has the shape of a triakis icosahedron.[3]

As a Kleetope[edit]

The triakis icosahedron can be formed by gluing triangular pyramids to each face of a regular icosahedron. Depending on the height of these pyramids relative to their base, the result can be either convex or non-convex. This construction, of gluing pyramids to each face, is an instance of a general construction called the Kleetope; the triakis icosahedron is the Kleetope of the icosahedron.[2] This interpretation is also expressed in the name, triakis, which is used for the Kleetopes of polyhedra with triangular faces.[1]

https://en.wikipedia.org/wiki/Triakis_icosahedron