In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron.[1]
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In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb...
to the short diagonals of the rhombi. The rhombic dodecahedron is a parallelohedron, a space-filling polyhedron, dodecahedrille, being the dual to the...
dodecahedron, it is a space-filling polyhedron, one of the five types of parallelohedron identified by Evgraf Fedorov that tile space face-to-face by translations...
generalization of a parallelepiped and parallelogram A generalization of a parallelohedron and parallelogon, this includes all parallelohedra in the first sense...
tessellate 3-dimensional space and is called a primary parallelohedron. Each primary parallelohedron is combinatorially equivalent to one of five types:...
the hexagonal prism, which classifies as an irregular octahedron and parallelohedron, is able to tessellate space as a three-dimensional analogue of the...
four-sided parallelogon is called a parallelogram. The faces of a parallelohedron (the three dimensional analogue) are called parallelogons. Quadrilateral...
different geometry than the face-transitive rhombic dodecahedron. It is a parallelohedron. This shape appears in a 1752 book by John Lodge Cowley, labeled as...
dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation. In addition to the...
Schenefeld near Hamburg. Group theory List of Russian material scientists Parallelohedron Zonohedron I. I. Shafranovskii and N. V. Belov, "In Memoriam: E. S...
within the hyperplane. The tessellation is the highest tessellation of parallelohedrons in 3-space. The bitruncated cubic honeycomb can be orthogonally projected...
plesiohedrons, defined as the Voronoi cells of a symmetric Delone set. Parallelohedrons are plesiohedra which are space-filling by translation only. Edges...
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