Distorting Jessen's Orthogonal Icosahedron to an Octahedron

Jessen's icosahedron is constructed by replacing six pairs of adjacent triangles in a regular icosahedron with pairs of isosceles triangles sharing a common base. There are six bases and they form three pairs of parallel edges.

This Demonstration varies the edges to distort the polyhedron until it closes up into a regular octahedron.