Pocket PUZZLE 2 - PENROSE — ARTOYA Learning Hub

Watch

See it come together

Assembly video coming — scan again after the next production run.

Read

The leaflet in the box

The same leaflet that comes with the kit, English on one side, French on the other. Free to download and print.

Download the leaflet (PDF)

ARTOYA_LEAFLET_AV0118114.pdf — 198 × 298 mm, EN/FR

Learn

Four ways in

Harmonices Mundi, Book II (De congruentia figurarum harmonicarum) — engraved plate of plane figures, pattern lettered 'Aa': pentagons, pentagrams, decagons and fused decagons (Kepler's 'monsters') — Johannes Kepler (1571–1630) — 1619 (Linz: Godefridus Tampachius / Johannes Plancus) — Smithsonian Libraries copy (Burndy Library), digitised on the Internet Archive, item ioanniskepplerih00kepl, leaf 78 (jp2, 1873 × 3054, 300 dpi) — Internet Archive ioanniskepplerih00kepl, leaf 0078

A Timeless History

A four-century puzzle. Squares and hexagons tile a floor; regular pentagons leave gaps. In 1619 Johannes Kepler drew pentagons, stars and decagons together in Harmonices Mundi and admitted the pattern needed 'monsters' — fused decagons — to go on. In 1966 a first set of tiles that could only tile without repeating was found: it needed more than 20,000 different shapes. In 1974 Penrose got the number down to two.

SourceNobel Prize in Chemistry 2011, Information for the Public · Nature Reviews Physics 6, 408 (2024) · Image: Kepler, Harmonices Mundi, Linz 1619, Book II plate, pattern 'Aa' — Internet Archive, Smithsonian Libraries (PD)

Ho-Mg-Zn dodecahedral quasicrystal, grown by the self-flux method (excess Mg), slowly cooled from 700 °C to 480 °C — on millimetre paper — Ames Laboratory, U.S. Department of Energy (Canfield group) — unknown (uploaded to Commons from cmp.ameslab.gov) — Wikimedia Commons, from the Ames Laboratory (US DOE) website — File:Ho-Mg-ZnQuasicrystal.jpg (548 × 464)

Science In Action

Aperiodic — the tiles cover the plane, but no arrangement of them ever repeats like wallpaper • Matching rules — marks on the edges force the order; ignore them and a dull periodic pattern appears • Fivefold symmetry — stars of five and ten appear everywhere, impossible in a repeating tiling • Golden ratio — in any large patch, fat rhombs outnumber thin ones by 1.618 to 1, never a whole number

SourceWolfram MathWorld, Penrose Tiles · Nobel Prize in Chemistry 2011, Information for the Public · Image: Ho-Mg-Zn quasicrystal, Ames Laboratory, U.S. Department of Energy (PD)

Imamzadeh Darb-i Imam, Isfahan, Iran — tiled vault of the portal (muqarnas and glazed tile mosaic) — Somayeh-Ra (Wikimedia Commons user), own work — 2021-05-05 — Wikimedia Commons — File:Imamzadeh Darb Imam-Isfahan-Iran.jpg (3872 × 2592)

Arts

Artisans got there first. By 1200 the craftsmen of Islamic Persia were building star-and-polygon patterns from a kit of five girih tiles. On the portal of the Darb-i Imam shrine in Isfahan, dated 1453, the large pattern is subdivided into a smaller copy of itself — the same self-similar trick Penrose used, five centuries earlier.

SourceLu & Steinhardt, Science 315, 1106 (2007) · Nobel Prize in Chemistry 2011, press release · Image: portal of the Darb-i Imam shrine, Isfahan — Wikimedia Commons, Somayeh-Ra (CC BY 4.0)

Playing with hat tiles (wheels) — laser-cut plywood copies of the Smith 'hat' aperiodic monotile, laid in wheels around hexagonal holes — Aschroet (Wikimedia Commons user), own work — 2023-07-22 — Wikimedia Commons — File:Playing with hat tiles (wheels).jpg (3731 × 2873)

Applications Today

Quasicrystals — in 1982 Dan Shechtman saw atoms packed like a Penrose pattern; Nobel Prize in Chemistry 2011 • Hard steel — quasicrystal grains armour a Swedish steel used for razor blades and eye-surgery needles • The 'hat' — in 2023 a single 13-sided tile was found that tiles only aperiodically; the search took 60 years

SourceNobel Prize in Chemistry 2011, press release and Information for the Public · Smith, Myers, Kaplan & Goodman-Strauss, arXiv:2303.10798 (2023) · Image: wooden hat tiles — Wikimedia Commons, Aschroet (CC0)

Penrose tiling: fat and thin rhombs — Wikimedia Commons

Did you know?

It never repeats.

Slide a Penrose pattern over a copy of itself: it never lines up again — yet every patch of it turns up elsewhere, infinitely often.

One more thing

The first set of tiles that could only tile without repeating, found in 1966, needed more than 20,000 different shapes. Penrose's set of 1974 needs two.

SourceNobel Prize in Chemistry 2011, Information for the Public (Royal Swedish Academy of Sciences)

Roger Penrose won the 2020 Nobel Prize in Physics — not for tiles, but for proving black holes can form.

Go deeper

The long read

A two-to-three-page article with more images and full explanations — printable. Coming for this model.

Build

How it comes together

Every part is cut and marked on the board; full instructions are on the sheet in the box. Once built, it stays built.

1

READ THE SHEET

Take your time — every detail counts. Check all the pieces are on the board.

2

ONE PIECE AT A TIME

Press out each piece only when the sheet calls for it.

3

THE TRAY

Base plate turned over, the two short rails, then the two long rails.

4

PIECES AND LID

Fourteen puzzle pieces into the tray, then the engraved lid slides on.

5

PAINT LAST

Once it stands — or keep it plain. No two are alike.

What it will not do

A puzzle, not a proof. Fourteen pieces, one rectangle, one tray. The lines on the pieces and the lid are engraved, not cut — no piece splits apart. Wood has a little play: a piece that 'almost' fits is not in, and the lid closes only when all fourteen are.

What it will give you

Why a pattern that never repeats makes a hard puzzle — the pieces are scraps of it, a tray leaves no room for 'nearly' — and why a 15th-century shrine, a metal alloy and a 2023 theorem share the same geometry.