Geometry Riddle: Try and Solve

Question

Consider a regular tetrahedron, T with side length 2a. At each corner, slice off a regular tetrahedron of side length a. What is left is an octahedron, P with side lengths a. Use this dissection to determine the volume of P in terms of a.

Please provide clear instructions, possibly a video if at all possible. Thanks.

Answer 1

The volume of the regular tetrahedron is 8a³.

From this you subtract the volume of 8 triangular pyramids with base edge of a√2 and slant edge of a.