Sphericons and D-forms: a crocheted connection

Abstract

Sphericons and D-forms are 3D objects created and described by artists, which have separately received attention in the mathematical literature in the last 15 or so years. The attempt to classify a seamed, crocheted form geometrically led to the observation, which appears not to have been previously made explicit, that these objects are related. General results concerning (N, k)-icons and seam-, D- and pita-forms are given. Instructions to crochet such forms are provided in the Appendix.

KEYWORDS:

• Sphericon
• D-form
• pita-form
• developable surface
• crochet
• AMS Subject Classification:
• 51M04
• 97M80

Acknowledgements

I wish to acknowledge the contributors to the thread How would you call this shape? in the Woolly Thoughts forum of Ravelry, in particular Annagret, bevbh, irishlacenet, MadeleineS, soyloquesoy and Woolhelmina, for their inspiration of this piece, and for pooling their collective wisdom about fibre arts and mathematics. Thanks also to Jane Pitkethly for creating four of the line drawings and to the fibre artists who permitted photos of their work to be used. Particular thanks to the estate of the late Steve Mathias for giving permission for photos of his wood-turning to be used, and to Craig Kaplan for Figure 3. The perceptive comments of editor and associate editor have also improved this paper significantly, and I thank them.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. It will become apparent that this author does not share this opinion.