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Interleaved Friezes: Celtic Knotwork and Hitomezashi

Katherine A. Seaton

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.

Interleaved Friezes: Celtic Knotwork and Hitomezashi

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.
Paper Structure (3 sections, 3 theorems, 3 equations, 13 figures, 2 tables)

This paper contains 3 sections, 3 theorems, 3 equations, 13 figures, 2 tables.

Table of Contents

  1. Two-Sided Friezes
  2. Celtic Knotwork Friezes
  3. Hitomezashi Friezes

Key Result

Theorem 1

None of the two-sided frieze patterns with the symbol 'm' in the fourth position can be realised in hitomezashi.

Figures (13)

  • Figure 1: Two hitomezashi friezes with glide reflection symmetry.
  • Figure 2: The two sides of a p1m1 hitomezashi frieze; $x=\overline{1110}$, $y=0110$. Compare with p1a1 in Figure 1 where $x=\overline{1000110}$, $y=100110$.
  • Figure 3: The two sides of a p11a hitomezashi frieze. $x=\overline{01}$, $y=0100$.
  • Figure 4: The two sides of a p11$\stackrel{2}{\textrm{a}}$ hitomezashi frieze. $x=\overline{10}$, $y=1010$. This is the traditional dan tsunagi (linked steps) stitch.
  • Figure 5: The two sides of a p112 hitomezashi frieze. $x=\overline{011001}$, $y=000$.
  • ...and 8 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof