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- W2328522781 abstract "Two sets of vertices ofa hypercubes in N and ~ are said to be equivalent if there exists a distance preserving linear transformation of one hypercube into the other taking one set to the other. A set of vertices'of a hypercube is said to be weakly rigid if up to equivalence it is a unique realization of its distance pattern and it is called rigid if the same holds for any multiple of its distance pattern. A method of describing all rigid and weakly rigid sets of vertices ofhypercube of a given size is developed. It is also shown that distance pattern of any rigid set is on the face of convex cone of all distance patterns of sets of vertices in hypercubes. Rigid pentagons (i.e. rigid sets of size 5 in hypercubes) are described. It is shown that there are exactly seven distinct types of rigid pentagons and one type of rigid quadrangle. It is also shown that there is a unique weakly rigid pentagon which is not rigid. An application to the study of all rind pentagons and quadrangles in L x having integral distance pattern is also given." @default.
- W2328522781 created "2016-06-24" @default.
- W2328522781 creator A5020142584 @default.
- W2328522781 date "1988-01-01" @default.
- W2328522781 modified "2023-09-23" @default.
- W2328522781 title "Rigid Pentagons in Hypereubes" @default.
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- W2328522781 hasPublicationYear "1988" @default.
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