In geometry, a plesiohedron is a special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set.
Three-dimensional Euclidean space can be completely filled by copies of any one of these shapes, with no overlaps. The resulting honeycomb will have symmetries that take any copy of the plesiohedron to any other copy.
The plesiohedra include such well-known shapes as the cube, hexagonal prism, rhombic dodecahedron, and truncated octahedron.
The largest number of faces that a plesiohedron can have is 38.
In geometry, a plesiohedron is a special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set. Three-dimensional Euclidean...
among others. Any polyhedron that fits this criterion is known as a plesiohedron, and may possess between 4 and 38 faces. Naturally occurring rhombic...
iteration Meyer set Pisot–Vijayaraghavan number Pitteway triangulation Plesiohedron Quasicrystal Quasitriangulation Salem number Steiner point (triangle)...
structure. As the Voronoi cell of a symmetric space pattern, it is a plesiohedron. For space-filling, the triakis truncated tetrahedron can be constructed...
2^{d+1}-2} facets, with the permutohedron achieving this maximum. A plesiohedron is a broader class of three-dimensional space-filling polyhedra, formed...
accurately be called stereotopes. A subset of stereohedra are called plesiohedrons, defined as the Voronoi cells of a symmetric Delone set. Parallelohedrons...
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