Dürer's Solid, also known as a truncated rhombohedron. The precise geometry of this form, as depicted by Dürer, is disputed. This version is designed to be inscribed inside a sphere. The acute angle on each pentagonal face is 72 degrees.
Several theories about this shape:
http://www.theguardian.com/science/alexs-adventures-in-numberland/2014/dec/03/durers-polyhedron-5-theories-that-explain-melencolias-crazy-cube
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