University of Cambridge
University of Cambridge: Nrich: Octa Space
At this one page web site see if you can solve this puzzle involving the edges of an octahedron. You will definitely need to use your problem solving and spatial reasoning skills for this!
Wolfram Research
Wolfram Alpha: Octahedron
The animation explores edge truncation of an octahedron and cube edges.
National Council of Teachers of Mathematics
The Math Forum: Angles of an Octahedron
This question and answer site from The Math Forum with Dr. Math discusses the angle between two adjacent faces of an octahedron. Links are also provided for additional information on related subjects.