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Voronoy polyhedron - translation to russian
геометрия
многогранник Вороного
![Full [[icosahedral symmetry]] divides the sphere into 120 triangular domains.](https://commons.wikimedia.org/wiki/Special:FilePath/Icosahedral reflection domains.png?width=200 "Full [[icosahedral symmetry]] divides the sphere into 120 triangular domains.")
![A skeletal polyhedron (specifically, a [[rhombicuboctahedron]]) drawn by [[Leonardo da Vinci]] to illustrate a book by [[Luca Pacioli]]](https://commons.wikimedia.org/wiki/Special:FilePath/Leonardo polyhedra.png?width=200 "A skeletal polyhedron (specifically, a [[rhombicuboctahedron]]) drawn by [[Leonardo da Vinci]] to illustrate a book by [[Luca Pacioli]]")
![The [[tetrahemihexahedron]], a non-orientable self-intersecting polyhedron with four triangular faces (red) and three square faces (yellow). As with a [[Möbius strip]] or [[Klein bottle]], a continuous path along the surface of this polyhedron can reach the point on the opposite side of the surface from its starting point, making it impossible to separate the surface into an inside and an outside.](https://commons.wikimedia.org/wiki/Special:FilePath/Tetrahemihexahedron rotation.gif?width=200 "The [[tetrahemihexahedron]], a non-orientable self-intersecting polyhedron with four triangular faces (red) and three square faces (yellow). As with a [[Möbius strip]] or [[Klein bottle]], a continuous path along the surface of this polyhedron can reach the point on the opposite side of the surface from its starting point, making it impossible to separate the surface into an inside and an outside.")
![Universum museum]] in Mexico City](https://commons.wikimedia.org/wiki/Special:FilePath/UniversumUNAM19.JPG?width=200 "Universum museum]] in Mexico City")
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Definition
Wikipedia
In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex. Cantellation also applies to regular tilings and honeycombs. Cantellating a polyhedron is also rectifying its rectification.
Cantellation (for polyhedra and tilings) is also called expansion by Alicia Boole Stott: it corresponds to moving the faces of the regular form away from the center, and filling in a new face in the gap for each opened edge and for each opened vertex.
