The rhombidodecahedral tessellation of 3-space and a particular 15-vertex triangulation of the 3-dimensional torus |
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Authors: | Wolfgang Kühnel Gunter Lassmann |
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Institution: | (1) Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D - 1000 Berlin 12 |
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Abstract: | It is well known that the unique 7-vertex triangulation of the 2-dimensional torus S1×S1 is a consequence of the relationship between two hexagonal lattices in the euclidean plane: it is just the quotient of the triangular tessellation of the plane by a translation group. Each vertex star is a regular hexagon and the symmetry group of this triangulation is the affine group A(1,7) in one dimension over 7. In this paper we describe a particular 15-vertex triangulation of the 3-dimensional torus S1×S1×S1 whose symmetry group is the affine group A(1,15) and which is similarly related to two lattices in euclidean 3-space: it is just the quotient of a particular tessellation of 3-space by a translation group. Each vertex star happens to be a rhombidodecahedron, the dual of a (semiregular) cuboctahedron. |
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