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## Main Question or Discussion Point

I made a certain star polyhedron out of Magnetix, and I'm trying to identify what its name is. It is formed by taking a regular icosahedron, and building a regular tetrahedron on each of its faces. Since an icosahedron has 20 faces, the resulting figure is a 20-pointed star. I've been looking in Wikipedia, which lists quite a lot of star polyhedra, but so far none of them match. The closest thing I could find was the great stellated dodecahedron, except that the great stellated dodecahedron has isosceles triangles as faces, while mine has equilateral triangles as faces.

Is there a name for my polyhedron, or has it not been named because the number of polyhedra are infinite?

Is there a name for my polyhedron, or has it not been named because the number of polyhedra are infinite?