DA VINCI DODECAHEDRON d12 — 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_AV0118104.pdf — 198 × 298 mm, EN/FR

Learn

Four ways in

Dodecaedron planum vacuum — hollow dodecahedron, woodcut after Leonardo's drawing, plate XXVIII of De divina proportione — Leonardo da Vinci (drawing); Luca Pacioli (author); printed Venice, Paganino Paganini — 1509 — Internet Archive scan divinaproportion00paci (same copy Commons uses for the Pacioli plates), leaf n244 — divinaproportion00paci, page n244

A Timeless History

Plato had four elements and five solids. He gave the dodecahedron to the cosmos itself — the god, he wrote, used it for the whole. Kepler took that literally in 1596 and nested the five solids inside one another to explain the solar system. He was wrong, and found the laws of planetary motion while trying to make it work. Leonardo had drawn it hollow for Pacioli in 1509 — the way this model is built.

SourcePlato, Timaeus (c. 360 BC) · Encyclopaedia Britannica — britannica.com · Johannes Kepler, Mysterium Cosmographicum (1596) · Encyclopaedia Britannica, “Johannes Kepler” · Luca Pacioli, De divina proportione, Venice 1509, plate XXVIII

Fer sulfuré (pyrite), Fig. 140 — the pentagonal dodecahedron (pyritohedron) crystal form, plate LXXVI of the Atlas of the Traité de minéralogie — René Just Haüy (author); Malouvre (engraver) — 1801 — Internet Archive scan traitdeminra05ha (Traité de minéralogie, tome 5, Atlas), leaf n174 — traitdeminra05ha, page n174

Science In Action

Twelve pentagonal faces, twenty vertices, thirty edges — 20 − 30 + 12 = 2, Euler's rule, true for all five • Dual of the icosahedron — twelve faces and twenty corners against twenty faces and twelve corners • Pentagons cannot tile — three around a corner leave a 36° gap; closing it forces the shape into 3D • Pyrite grows twelve-faced too, but its pentagons are not regular — mineralogists call it a pyritohedron

SourceEncyclopaedia Britannica, “polyhedron” · Euclid, Elements, Book XIII · Mathematical Association of America, Convergence — maa.org · Wolfram MathWorld, “Pyritohedron” — mathworld.wolfram.com · Encyclopaedia Britannica, “pyrite”

The dodecahedron filled with the cosmos (a face-on sun and stars) — detail of the engraved plate of the regular solids and their elements, Harmonices Mundi, Book II — Johannes Kepler — 1619 — Smithsonian Libraries copy, Internet Archive scan ioanniskepplerih00kepl, leaf n80 (same plate as Commons 'Ioanniskepplerih00kepl 0081.jpg') — ioanniskepplerih00kepl, page n80

Arts

Kepler's 1619 woodcut fills the dodecahedron with a face-on sun and a sky of stars — the only one of his five that gets the whole cosmos rather than an element. It is a picture of an idea rather than a thing, which is why it has outlasted the theory it illustrated.

SourceJohannes Kepler, Harmonices Mundi (Linz, 1619), Book II — Smithsonian Libraries copy

Pentagon-dodecahedron in bronze, 150–400 AD, found Tongeren, Leopoldwal, 1939 — Gallo-Roman Museum Tongeren inv. 4002 — Gallo-Romeins Museum Tongeren (photograph); unknown Roman maker — 150–400 AD (photo released by the museum) — Wikimedia Commons (museum upload) — File:Pentagon-dodecaëder in brons, 150 tot 400 NC, vindplaats- Tongeren, Leopoldwal, 1939, collectie Gallo-Romeins Museum Tongeren, 4002.jpg

Applications Today

More than a hundred hollow bronze dodecahedra have been dug up across Roman Gaul and Britain, each with different-sized holes in the faces. Surveying instrument, knitting frame, calendar, ritual object — every explanation proposed, none proven.

SourceThe British Museum — britishmuseum.org · Encyclopaedia Britannica

A Roman dodecahedron — Hunt Museum, Limerick

Did you know?

Over a hundred, and nobody knows why

Bronze Roman dodecahedra keep turning up across northern Europe. No Roman text mentions them, and nobody knows why.

One more thing

Kepler tried to explain the spacing of the planets by nesting these five solids. The theory was wrong. Chasing it gave him the laws of planetary motion.

SourceEncyclopaedia Britannica, “Johannes Kepler”

Plato gave this one to the universe. We have not finished arguing about it since.

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 CORE

Two big fins cross-slot into each other, two ribs lock them: the core.

4

THE TWELVE FACES

Faces go on in pairs, turning the core over as the sheet shows.

5

PAINT LAST

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

What it will not do

It is not a gaming die. The open frame and the wood grain mean it will not roll fairly. It is a geometric model, built to show the shape.

What it will give you

Faces, edges and vertices we can count on our fingers; why exactly five regular solids can exist and no more; and how an open frame reveals what holds it up.

Assembly instructions

Lost the sheet? Enter the box code printed inside the sleeve (product code + last 4 digits of the barcode) to download the instructions.

Teach

Lesson plan

Free with the code printed inside your box, or $4.95 on its own. Teachers: sign in for the full pack — plan, worksheet, answer key.

Grade band: 8–12
Duration: 90 min
Standards: MS-ETS1-1MS-PS2-2MS-PS3-16.G.A.47.G.A.37.G.B.6HSG-GMD.A.1VA:Cr2.1.8aVA:Cn11.1.HSI1.4
UK: KS3 Maths — 3-D shapes, nets · KS3 D&T — mechanical systems