Interleaved Friezes: Celtic Knotwork and Hitomezashi

TL;DR

This paper investigates the relationship between Celtic knotwork and hitomezashi stitching, analyzing which two-sided friezes can be realized in hitomezashi and comparing it to Celtic knotwork, with proofs and classifications.

Contribution

It provides a complete classification of two-sided friezes realizable in hitomezashi and compares these to Celtic knotwork, establishing new theoretical results.

Findings

Identifies which of the 31 two-sided friezes can be realized in hitomezashi

Provides proofs distinguishing realizable and non-realizable friezes

Establishes a comparison framework between hitomezashi and Celtic knotwork

Abstract

Both Celtic knotwork and strips of hitomezashi stitching can be interpreted as being two-sided friezes wherein the patterns on the sides are interleaved. We prove which of the thirty-one two-sided friezes can, and cannot, be realized in hitomezashi, and compare this to the case of Celtic knotwork.