More Answers to Polyhedron Challenge 6

Start with a cube. It has 8 vertices. At each vertex, slice off a piece of the cube; your slice should go through the midpoints of the edges you are slicing. The face left after one vertex is sliced off is a triangle, and the piece removed is a tetrahedron. Since you cut off 8 vertices, you will have 8 triangles. Parts of each of the original 6 square faces are still left. In fact, they are smaller squares, whose vertices are the midpoints of the edges of the original squares.

Before slicing, with slice lines marked.

After slicing.

Start with an octahedron. It has 6 vertices. At each vertex, slice off a piece of the octahedron; your slice should go through the midpoints of the edges you are slicing. The face left after one vertex is sliced off is a square, and the piece removed is a square pyramid. Since you cut off 6 vertices, you will have 6 squares. Parts of each of the original 8 triangular faces are still left. In fact, they are smaller triangles, whose vertices are the midpoints of the edges of the original triangles.

Before slicing, with slice lines marked.

After slicing.