The Canon · Folio One
Plate XXIX of XXIX
The Aperiodic Monotile
One shape that never repeats, found by a retired print technician.
Paper ground, a warm cream, on Hahnemühle Photo Rag, 308 gsm cotton
The plate
David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss, An aperiodic monotile · 2023
An einstein, from the German ein Stein, one stone, is a single shape that tiles the plane but never repeats. Since the 1960s, such tilings had always needed sets of shapes, from Robert Berger’s 20,426 down to Roger Penrose’s two. Then Smith, a retired print technician in East Yorkshire, found one in November 2022: the hat, eight kites from a hexagonal grid. The blue are mirror images, outnumbered by the golden ratio to the fourth power; the yellow meet in threes and branch like trees.
Computed, not drawn: every mark on the plate comes from the mathematics or from real data, and the type is set from the same files that go to the printer.
The tiling is generated with a port of Craig S. Kaplan’s hatviz (BSD 3-Clause licence, © 2023 Craig S. Kaplan).
Sizes and prices
| Size | Unframed | Framed | |
|---|---|---|---|
| Small30 × 42 cm | £50$85 | £140$185 | 297 × 416 mm |
| Medium50 × 70 cm | £110$165 | £350$465 | 500 × 700 mm |
| Large70 × 98 cm | £190$255 | £520$695 | 700 × 980 mm |
- Paper: Hahnemühle Photo Rag, 308 gsm cotton, printed as a giclée by theprintspace.
- Printed in: London for the UK, Brooklyn for the US. Unframed prints travel rolled in a tube.
- Framed small: A3 (29.7 × 42 cm) frame, glazed with glass.
- Framed medium: 60 × 80 cm frame with a 5 cm window mount, glazed with 3 mm acrylic.
- Framed large: 70 × 100 cm frame, glazed with 3 mm acrylic.
- Frames: black, white or oak, solid wood, made in Germany. Each comes ready to hang.
- Edition: open, with a certificate. File version v1.