This is an icosahedron because it has twenty faces, and it is of tetrahedral symmetry. There are four regular hexagons and four equilateral triangles among these faces, along with twelve isosceles triangles with a leg:base length ratio of 1.73205:1. I found it while investigating variations to the base/dual compound of the truncated tetrahedron using *Stella 4d*, which you can try for free at this website. This polyhedron is the dual of the convex hull of the base/dual compound of the truncated tetrahedron and the triakis tetrahedron.

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Thanks for posting the ratio of the leg-base ratio in advance of my having to ask. I am currently on the last lap of a long-term project. When that is finsihed, I will be building paper models of many small ones that you have posted about.

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