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

**Solution**

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 .

**Answer**:

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Retired high school math teacher.