Icosahedron
There are two objects, one convex and one concave, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have the same symmetry so that their vertices are at similar places. The term "regular icosahedron" usually refers to the convex icosahedron, while the nonconvex form is called a great icosahedron.