Textile D forms and $D_{4d}$

TL;DR

This paper explores the creation of textile D-forms and pita-forms, demonstrating their practical applications and ornamental uses, including a biscornu sampler illustrating the axial point group D_{4d} and its subgroups.

Contribution

It introduces new textile realizations of D-forms and pita-forms, including a biscornu sampler that visualizes the D_{4d} symmetry group through embroidery.

Findings

Textile D-forms can be purposefully employed in 3D space.

Ornamental surface decoration enhances the visual appeal of textile forms.

A biscornu was created as a 3D sampler of the D_{4d} symmetry group.

Abstract

D-forms have in the past been created from inflexible materials, or considered as abstract mathematical objects. This paper describes a number of realisations of D-forms, and the related pita-forms, in textiles. Examples are given in which the created 3D space is purposefully employed and others in which ornamentation of the constituent surfaces is the highlighted feature. In particular, a set of biscornu has been fashioned to provide a 3D sampler of the axial point group $D_{4d}$ and its subgroups, using hitomezashi.