All corners were sliced off a cube whose volume was cubic centimeters. Triangular faces are located where the cube’s vertices were. Each triangle is equilateral with -centimeter sides. Determine the total numbers of edges on the new solid.
Source: NCTM Mathematics Teacher, January 2006
A cube has edges and vertices. If each vertex is sliced off and replaced by a triangle, more edges are added on the new solid. Thus, the total number of edges equals .