Polyhedral orbits in Oh point symmetry

We believe J.W. Linnett, in his Methuen Monograph, Wave Mechanics and Valency Theory, 1956, was the first to use elliptical projections to display the phases of the spherical harmonics on the unit sphere. We adopt a projection in which both 0 and (f) coordinates are plotted on linear scales on the minor and major axes of a 30° ellipse of eccentricity a/3/2. This cartographic device is the one proposed by Apianus in 1524, and known as the Apianus II projection. In our early work on the Spherical Shell method we called this a modified Mollweide projection, reversing the historical sequence. 

A continuous range of equisymmetric structures is permitted. Within that range, the other Archimedean polyhedra based on cubic geometry appear, in turn, as the local sets of vertices about the principal rotational axes are allowed to coalesce. 

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