38 citations · 77 across the 5 of their papers we have counts for
6 papers
A chiral aperiodic monotile
David Smith, Joseph Samuel Myers, Craig S. Kaplan +1
The recently discovered "hat" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperi…
An aperiodic monotile
David Smith, Joseph Samuel Myers, Craig S. Kaplan +1
A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this proble…
Freeform Islamic Geometric Patterns
Rebecca Lin, Craig S. Kaplan
Islamic geometric patterns are a rich and venerable ornamental tradition. Many classic designs feature periodic arrangements of rosettes: star shapes surrounded by rings of hexagon…
Heesch Numbers of Unmarked Polyforms
Craig S. Kaplan
A shape's Heesch number is the number of layers of copies of the shape that can be placed around it without gaps or overlaps. Experimentation and exhaustive searching have turned u…
A Frameless 2-Coloring of the Plane Lattice
Craig S. Kaplan, Jeffrey Shallit
A picture frame in two dimensions is a rectangular array of symbols, with at least two rows and columns, where the first and last rows are identical, and the first and last columns…
Quasiperiodic bobbin lace patterns
Veronika Irvine, Therese Biedl, Craig S. Kaplan
Bobbin lace is a fibre art form in which threads are braided together to form a fabric, often with a very detailed and complex design. In traditional practice, each region of the f…