Sphericons and D-forms: a crocheted connection

TL;DR

This paper explores the geometric relationship between sphericons and D-forms, two artistic 3D objects, providing a classification framework and crochet instructions, thus bridging art and mathematics.

Contribution

It introduces a geometric classification linking sphericons and D-forms, and offers crochet instructions, highlighting their mathematical connection.

Findings

Sphericons and D-forms are related geometrically.

A classification scheme for seam-, D-, and pita-forms is proposed.

Crochet instructions for D-forms are provided.

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.