File:Plastic pentagons alt.svg

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Summary

Description
English: Pentagons tiled by whorls of equilateral triangles with sides in plastic ratio ρ, satisfying ρ3 = ρ + 1. The polar slope of the logarithmic spirals is 3/πln(ρ), corresponding to angle 74°58'. Relative to the left-hand base vertex, each pole has Cartesian coordinates (ρ7/2(ρ + 2), √3/2(ρ + 2)). This arrangement was discovered in 1949 by John Rutherford Boyd, searching for spirals which touch multiple times.
For a similar figure, see:
A triskeles of plastic pentagons
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Author Zilverspreeuw
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Captions

Pentagon spirals in Rutherford Boyd's design.

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7 June 2025

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current11:57, 7 June 2025Thumbnail for version as of 11:57, 7 June 2025500 × 500 (4 KB)wikimediacommons>ZilverspreeuwUploaded own work with UploadWizard

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