The Molecular Tactics of a Crystal

Cover The Molecular Tactics of a Crystal
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This problem is determinate, because the making of the three contacts f'f, g'g, h'h, uses up the three independent variables left at our disposal after we have first formed a homogeneous assemblage with twelve points of contact on each solid. But our manner of finding a shape for each solid which can allow the solution of the problem to be real, proves that the solution is essentially imaginary for every wholly convex shape.
35. Pausing for a moment longer to consider afresh the geometrical pro
...blem of putting arbitrarily given MOLECULAR TACTICS OF A CRYSTAL 39 equal and similar solids together to make a homoge- neous assemblage of which each member is touched by eighteen others, we see immediately that it is determinate (whether it has any real solution or not), because when the shape of each body is given we have nine disposables for fixing the assemblage: six for the character of the assemblage of the correspond- ing points, and three for the orientation of each molecule relatively to rows of the assemblage of corresponding points.

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