Icosahedral Slices (Tri-Pent Polyhedra)
I discovered an interesting shape: an octahedron made of three regular pentagons and five equilateral triangles. I've never seen this shape before and don't know if it has a name, so I'm calling it the Tri-Pent Octahedron. It has the interesting property that if you replace each pentagon with five equilateral triangles you get an icosahedron. Several other shapes have this property, including the pentagonal antiprism and a pentagonal pyramid. There's another shape with 15 triangles and one pentagon, and yet another still with two pentagons and 10 triangles, but it's not an antiprism because the pentagons are not in parallel planes. Here are CP's for the complete set of shapes "Icosahedra with One or More Slices Cut Out of Them, Whose Faces are Composed of Pentagons and Triangles."