Using only the vertices of a regular octahedron as the corners, how many equilateral triangles in total is it possible to make?

(In reply to My guess by tomarken)

Agree. At each of the 6 vertices, four of the others are the same distance and form only faces of the octahedron (or isosceles triangles  across the square cross-section).  The remaining vertex is at a unique distance (for the given original vertex) and can't form an equilateral triangle.

Posted by Charlie on 2014-07-28 17:33:02