From each vertex of a regular octahedron of edge length 6 units, a square-based pyramid of height 1 unit will be cut away. How many vertices will the new solid have?
The octahedron currently has 6 vertices. Each removal of a square-based pyramid removes one vertex and adds 4 more; this occurs 6 times. Hence we end up with 4 times 6= 24 vertices.
