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Building a better bracelet: wallpaper patterns in bead crochet. (English) Zbl 1287.52014

Summary: A typical bead crochet bracelet consists of a narrow tube of seed beads sewn together to form an uninterrupted hollow band. Creating symmetric colour patterns on bead crochet bracelets is challenging because the beads form a continuous spiral along the length of the bracelet, making it difficult to align design motifs uniformly. We have devised a new technique for translating bracelet patterns into plane tilings and used this to create bracelets based on wallpaper group symmetries to stunning effect. We prove that exactly 13 of the 17 wallpaper groups can be represented by bead crochet bracelets, and we outline a general method for designing a bracelet whose planar bead tiling has a given wallpaper symmetry group.

MSC:

52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
00A66 Mathematics and visual arts
20H15 Other geometric groups, including crystallographic groups
Full Text: DOI

References:

[1] Bertoglio-Giffin J, Bead Crochet Ropes (2002)
[2] Bertoglio-Giffin J, Patterns & Graphing for Bead Crochet Ropes (2004)
[3] Bertoglio-Giffin J, CreateSpace, Charleston, SC, (2011)
[4] Conway JH, The Symmetries of Things (2008)
[5] Kerrigan S, Shala’s Beadwork and other crafty and artsy things.
[6] DOI: 10.1080/17513470903196177 · doi:10.1080/17513470903196177
[7] Washburn D, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis (1988) · Zbl 1202.01004
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