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Distorting Jessen's Orthogonal Icosahedron to an Octahedron

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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.
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