Titlebook: Space Structures; Arthur L. Loeb Book 1991 Arthur L. Loeb 1991 Statistica.boundary element method.form.group.mathematics.society.symmetry

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Valencies,y by comparison with Fig. 2-2, which represents the number 1. The appearance of a single unique point at once establishes a center of reference. The extension to Fig. 2-3, the number 2, is stupendous: instead of a single central point we have now . vertices, between which there can be a relation. Th

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Statistical Symmetry,valencies of these elements toward each other. We have seen, furthermore, that the numbers of elements of different dimensionality are interrelated by the Euler-Schlaefli relation (equations 3-1 and 3-2), and that the valencies are restricted by two relations derived from the Euler-Schlaefli relatio

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Degrees of Freedom,tex can move with . degrees of freedom, whereas on a curve (dimensionality .) it can move with only a single degree of freedom. In three-dimensional space a vertex has three degrees of freedom: three quantities are needed to specify its location.

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Lattices and Lattice Complexes,by moving the entire lattice parallel to itself through an appropriate distance it can be brought into coincidence with itself (cf. Fig. 15-1). It follows that a lattice is infinite in extent. The points of any planar lattice may constitute the centers of hexagonal Dirichlet Domains; we saw in the p

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Additional Space Fillers and their Lattice Complexes,be, truncated octahedron, and rhombohedral dodecahedron—fill space; all three have the maximum symmetry. There are, in addition, interesting lattice . whose Dirichlet Domains also, of course, fill space. Since the environments of lattice-complex points are identical, but not necessarily oriented par

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