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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: * It is vertex-transitive (or ''isogonal''), meaning that it has symmetries taking any vertex to any other vertex. * It has only right dihedral angles. * It is (continuously) rigid but not infinitesimally rigid. That is, in less formal language, it is a shaky polyhedron. * As with the simpler Schönhardt polyhedron, its interior cannot be triangulated into tetrahedra without adding new vertices. * It is scissors-congruent to a cube, meaning that it can be sliced into smaller polyhedral pieces that can be rearranged to form a solid cube. 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 == * The Fifty-Nine Icosahedra == References == * 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jessen's icosahedron」の詳細全文を読む スポンサード リンク
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