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Full-Text Articles in Physical Sciences and Mathematics
Tilings By Hexagonal Prisms And Embeddings Into Primitive Cubic Networks, Mikhail M. Bouniaev, Nikolay Dolbilin, Mikhail I. Shtogrin
Tilings By Hexagonal Prisms And Embeddings Into Primitive Cubic Networks, Mikhail M. Bouniaev, Nikolay Dolbilin, Mikhail I. Shtogrin
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
All possible combinatorial embeddings into primitive cubic networks of arbitrary tilings of 3D space by pairwise congruent and parallel regular hexagonal prisms are discussed and classified.
Embedding Parallelohedra Into Primitive Cubic Networks And Structural Automata Description, Mikhail M. Bouniaev, Sergey V. Krivovichev
Embedding Parallelohedra Into Primitive Cubic Networks And Structural Automata Description, Mikhail M. Bouniaev, Sergey V. Krivovichev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The main goal of the paper is to contribute to the agenda of developing an algorithmic model for crystallization and measuring the complexity of crystals by constructing embeddings of 3D parallelohedra into a primitive cubic network (pcu net). It is proved that any parallelohedron P as well as tiling by P, except the rhombic dodecahedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodecahedron embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net exists. The question of how many ways the embedding of a parallelohedron can …