Simple edge forms of the cubic singony
Abstract
The present communication completes the series of articles by V. I. Mikheev and I. I. Shafranovsky devoted to the complete derivation of all possible edge forms. In the derivation of simple edge forms of the cubic system, we first of all proceed from possible facet combinations. For this purpose we had to enumerate all possible pairwise combinations separately for each of the five kinds of symmetry. The symbols for such combinations are summarized in the table, where the upper horizontal line contains the symbols of the faces of the initial forms, in the planes of which lie the derived edges. The vertical line contains combinations of symbols of those faces, the intersection of which results in edge forms. A number of edge forms with a relatively small number of included edges are the result of intersection of faces of one simple form (from among those indicated in the upper horizontal row of the table); for example, the dodecahedron of the cube.
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References
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