Fibonacci Tetrahedron

Recall that the Fibonacci numbers are defined as follows:

F1 = 1
F2 = 1
Fn = Fn-1 + Fn-2 for n > 2

For a given positive integer n, what is the volume of the tetrahedron which has vertices (Fn, Fn+1, Fn+2), (Fn+1, Fn+2, Fn+3), (Fn+2, Fn+3, Fn+4) and (Fn+3, Fn+4, Fn+5)?

Solution