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Tiling space and slabs with acute tetrahedra. (English) Zbl 1054.65020
An acute tetrahedron has all its interior dihedral angles strictly less than a right angle. So far, of all known space tilings with congruent copies of a single tetrahedron, none use acute tetrahedra. This paper shows how an Euclidean space can be tiled with acute tetrahedra if several shapes of tetrahedra are used simultaneously. Three types of constructions are presented that achieve this result: the first family of tilings is taken from crystallography, the second construction uses a regular icosahedron lattice, and the third is based on tiling a slab in space. Due to the quality of their tetrahedron components (measured in terms of the radius-edge ratio and the extreme dihedral angles), these constructions are well suited for applications to mesh generation.

MSC:
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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