----- On Sun, Sep 25, 2016 at 12:01 PM, Hans Havermann wrote:

...

"The volume of a regular tetrahedron (triangular pyramid with unit edges) is exactly half the volume of a square pyramid with unit edges."

This is (I think) equivalent to stating that the volume of an octahedron is four times the volume of a tetrahedron (unit edges assumed).

. . . At some point after the above time Andy Latto wrote: The geometrical "proof" of this is that you can assemble 4 unit tetrahedrons and a unit octahedron to produce a tetrahedron with edge length two, and therefore area equal to 8 tetrahedrons. ----- Lovely proof, Andy. Much better than doing the calculation (though it was fun doing it in my head). —Dan