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Electronic Geometry Models
2008-05-13
ZMATH includes now the items of the Electronic Geometry Models archive, like the Rhombicosidodecahedron (one of the thirteen Archimedean solids, with 60 vertices, 120 edges and 62 facets, 12 pentagons, 30 squares and 20 triangles), or Sharir's cube.
As Günther M. Ziegler describes in Zbl 1133.52302, the latter is "a 3-cube with the property that each facet is perpendicular to its opposite. Micha Sharir asked the question whether such a cube exists. This construction solves the problem in the affirmative. It is fairly obvious that no such cube (quadrangle) exists in 2 dimensions. On the other hand, the present example in dimension 3 can be used to lift the construction to higher dimensions.
