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Jessen's icosahedron

Jessen's icosahedron
Faces
Edges
  • 24 short and convex
  • 6 long and concave
Vertices12
Dihedral angle (degrees)90
Properties
Net

Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same numbers of vertices, edges, and faces as the regular icosahedron. It is named for Børge Jessen, who studied it in 1967.[1] In 1971, a family of nonconvex polyhedra including this shape was independently discovered and studied by Adrien Douady under the name six-beaked shaddock;[2][3] later authors have applied variants of this name more specifically to Jessen's icosahedron.[4]

The faces of Jessen's icosahedron meet only in right angles, even though it has no orientation where they are all parallel to the coordinate planes. It is a "shaky polyhedron", meaning that (like a flexible polyhedron) it is not infinitesimally rigid. Outlining the edges of this polyhedron with struts and cables produces a widely-used tensegrity structure,[5] also called the six-bar tensegrity,[6] tensegrity icosahedron, or expanded octahedron.[7]

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