Jessen's icosahedron

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The regular icosahedron and the Jessen's icosahedron.

Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same number of vertices, edges and faces as the regular icosahedron. It was introduced by Børge Jessen in 1967 and has several interesting geometric properties:

Although a shape resembling Jessen's icosahedron can be formed by keeping the vertices of a regular icosahedron in their original positions and replacing certain pairs of equilateral-triangle faces by pairs of isosceles triangles, the resulting polyhedron does not have right-angled dihedrals. The vertices of Jessen's icosahedron are perturbed from these positions in order to give all the dihedrals right angles.

See also[edit]


  • B. Jessen, Orthogonal Icosahedra, Nordisk Mat. Tidskr. 15 (1967), pp. 90–96.
  • Peter R. Cromwell, Polyhedra, Cambridge University Press, (1997) pp. ?
  • M. Goldberg, Unstable Polyhedral Structures, Math. Mag. 51 (1978), pp. 165–170
  • Wells, D. The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin, (1991). p. 161.

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