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 D-forms are given in the Appendix.

11 pages, 12 figures; submitted to Journal of Mathematics and the Arts; Revised version uploaded June 15, 2016 Revised version of Jan 6, 2017 contains 17 figures and 14 pages; Further revision (as accepted by Journal) uploaded March 2017

Cited by in corpus (2)

• Textile D forms and $D_{4d}$
• The polycons: the sphericon (or tetracon) has found its family