Abstract
In this talk, we discuss tessellabilities, reversibilities, and decomposabilities of polygons, polyhedra, and polytopes, where by the word “tessellability”, we mean the capability of the polytope to tessellate. Although these three concepts seem quite different, but there is a strong connection linking them. These connections will be shown when we consider the lattices of tilings in ℝ2 and tessellations in ℝ3, which can be regarded as discrete metric spaces. Many old and new results together with various research problems will be presented.
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Akiyama, J., Sato, I., Seong, H. (2013). Tessellabilities, Reversibilities, and Decomposabilities of Polytopes. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_22
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DOI: https://doi.org/10.1007/978-3-642-40020-9_22
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