Crocheting an Isomorphism between the Automorphism Groups of the Klein Quartic and Fano Plane

Year: 2021 Authors: Shintaro Fushida-Hardy

Core claim

The crochet model makes the automorphism groups of the Klein quartic and Fano plane visibly match, yielding an explicit isomorphism PSL(2,7) → PSL(3,2).

Topics

exceptional isomorphism, automorphism groups, crochet geometry, Fano plane, Klein quartic

Domains

finite group theory, projective special linear groups, hyperbolic geometry, finite geometry, fiber art, textile sculpture, color encoding, mathematical craft

Methods

crochet construction, color-based labeling, symmetry inspection, group action comparison

Media

single-crochet stitches, black yarn, colored yarn, stitched equilateral triangles

Source status

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