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With A vertices as its "poles," the 60 other vertices of the disdyakis triacontahedron are
corners of seven polygons. With C vertices as poles, the 60 vertices are corners of
**15** polygons. They are shown here divided into their sectors. The sides of the seven polygons
are edges of the polyhedron apart from the six sides of the 6-sided polygon and the two vertical sides of the
10-sided polygon. None of the sides of the **15** polygons are polyhedral edges because the
corners in a given polygon are all the same type of vertex (A, B or C). The significance of these facts will emerge
in the discussion in **Superstrings as sacred
geometry/Disdyakis triacontahedron** of how the sets of seven and
**15** polygons encode the three-dimensional structure and group dynamics of the
E_{8}×E_{8} heterotic superstring.

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