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Figure 9
Geometry of the central polygon for the octagonal, decagonal and dodecagonal twin shown top left, middle right and bottom left, respectively. Highlighted in each case as open circles are the origin O as well as the points P00, P10 and P01, whose relative location (in the graph-theoretical sense) is the same for all depicted cases, as is the absolute distance of unity between the points P00 and P01. The circumcircle radii R and edge lengths E differ, however. Note that in the decagonal case the edge length equals the distance between the points P00 and P01, and that the circumcircle radii correspond to the respective scaling factors, [R = \tau_{m}]. Points highlighted as solid circles depict unit distance connections between adjacent spiral branches and to the origin, with their rotationally equivalent points omitted for clarity. Unit distance lines are shown with greater thickness.

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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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