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Figure 6
Derivation of the factor [\tau_{m}] for the cases of m = 8 (left) and m = 12 (right). Shown are the central polygons of the CSCTs together with a triple of mutually adjacent rhombs. The triple is composed of a pair of thin rhombs oriented towards the center and a single thick rhomb at the periphery. The thin rhombs have an acute angle of [\alpha = 2\pi /m] (dark gray), which corresponds to half of the acute angle of a single thick rhomb, which, in the special case of m = 8, corresponds to half of a right angle of a square. A right triangle (light gray) can be constructed and used to determine the length of a segment of the circumcircle radius (thick line) of the polygon to be equal to [e\cos\alpha], in which e denotes the edge length of a rhomb. Then, the total circumcircle radius is equal to [R = e+2e\cos\alpha], and for e set to unity, [\tau_{m} = 1+2\cos\alpha] follows.

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ISSN: 2053-2733
Volume 78| Part 1| January 2022| Pages 21-35
https://doi.org/10.1107/S2053273321012237
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