What is the Name of My Star Polyhedron?

[lugita15]

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?

 

[tiny-tim]

Hi lugita15!

Does this help … http://mathworld.wolfram.com/IcosahedronStellations.html" ?

 

[lugita15]

Hi lugita15!

Does this help … http://mathworld.wolfram.com/IcosahedronStellations.html" ?

Unfortunately, I don't think that my polyhedron is a stellation of an icosahedron. The definition of stellation in mathworld is "the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect." This is not the case for my polyhedron. This is because faces of the tetrahedra do not lie in the same planes as any of the faces of the icosahedron.

In order to clarify what I am talking about, I have attached two pictures, one of a plain old icosahedron, and one of the star polyhedron I am trying to identify. As you can see, each of the faces of each of the tetrahedra (except, of course, the faces which coincide with the icosahedron faces) makes obtuse angles with icosahedron faces adjacent to it.

As I mentioned in my first post, the polyhedron I'm looking for is extremely similar to the great stellated dodecahedron, and is in fact a deformed version of the latter.

I apologize if my terminology is imprecise; I don't know much about 3-D geometry.