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What is Parallelohedron in Three-Dimensional Space

Chapter 8
Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
A polyhedron capable of filling a three-dimensional space without gaps during its translation, with adjacent polyhedrons adjacent to each other along whole flat faces of the polyhedrons.
Published in Chapter:
Parallelohedrons of Higher Dimension and Partition of N-Dimensional Spaces
Copyright: © 2021 |Pages: 42
DOI: 10.4018/978-1-7998-6768-5.ch008
Abstract
For more than 100 years in science, many researchers, when trying to solve Hilbert's 18th problem of constructing n-dimensional space, used the principles of the Delaunay geometric theory. In this book, as a result of a careful analysis of the work in this direction, it is shown that the principles of the Delaunay theory are erroneous. They do not take into account the features of figures of higher dimensionality, do not agree with modern advances in the physics of the structure of matter, and lead to erroneous results. A new approach to solving the 18th Hilbert problem is proposed, based on modern knowledge in the field of the structure of matter and the geometric properties of figures of higher dimension. The basis of the new approach to solving the 18th Hilbert problem is the theory developed by the author on polytopic prismahedrons.
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