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Square-Triangle Tilings: Lift & Flip to Sample?

Thomas Fernique, Olga Mikhailovna Sizova

Abstract

We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.

Square-Triangle Tilings: Lift & Flip to Sample?

Abstract

We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.

Paper Structure

This paper contains 4 sections, 2 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Lift
  3. Flip
  4. Flip-connectivity

Figures (6)

  • Figure 1: Two square-triangle tilings of the same region.
  • Figure 2: The vectors which define tiles (left) and the conditions on their lifts.
  • Figure 3: Square-triangle tilings with the height of every vertex indicated.
  • Figure 4: A flip.
  • Figure 5: A flip seen in the lift.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Conjecture 1