DA VINCI TETRAHEDRON d4 — 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_AV0118101.pdf — 198 × 298 mm, EN/FR

Learn

Four ways in

The five regular solids paired with the elements (octahedron/air, tetrahedron/fire, dodecahedron/cosmos, cube/earth, icosahedron/water), engraved plate in Harmonices Mundi libri V, Book II — Johannes Kepler (Linz: Tampach / Plancus) — 1619 — Smithsonian Libraries (Burndy Library) scan on the Internet Archive — ioanniskepplerih00kepl, leaf 80

A Timeless History

Plato set out the five regular solids in the Timaeus around 360 BC and matched each to an element. The tetrahedron got fire — the sharpest and most mobile. Around 300 BC Euclid closed the Elements by proving these five are the only ones that can exist. Kepler drew the pairing in 1619: flames inside the tetrahedron, birds in the octahedron, a sun in the dodecahedron.

SourcePlato, Timaeus (c. 360 BC) · Encyclopaedia Britannica — britannica.com · Euclid, Elements, Book XIII · Mathematical Association of America, Convergence — maa.org · Johannes Kepler, Harmonices Mundi (Linz, 1619)

[Tetrahedral tower at Baddeck, Nova Scotia] — Alexander Graham Bell's tower built of tetrahedral cells — Gilbert H. Grosvenor Collection of Alexander Graham Bell photographs (photographer unrecorded) — [1906] as catalogued; the tower was raised in 1907 — Library of Congress, Prints & Photographs Division — LC-G9-Z1-116,448-A · LOT 11533-A66-42

Science In Action

Four vertices, six edges, four faces: 4 − 6 + 4 = 2, Euler's rule, true for every solid in this set • Self-dual — its own face-centres make another tetrahedron • Rigid — a triangle cannot change shape without changing the length of a side • The stiffest frame you can build from struts — Bell built kites and a tower from tetrahedral cells

SourceEncyclopaedia Britannica, “polyhedron” · Euclid, Elements, Book XIII · Library of Congress, Prints & Photographs — loc.gov

Tetraedron planum vacuum — hollow tetrahedron, woodcut after Leonardo's drawing, De divina proportione — Leonardo da Vinci (drawing); Luca Pacioli (author); printed Venice, Paganino Paganini — 1509 — Wikimedia Commons (scan from the Internet Archive, divinaproportion00paci) — File:De divina proportione - Tetraedron Planum Vacuum.jpg

Arts

Leonardo drew all five solids for Luca Pacioli's De divina proportione in 1509 — each one twice, solid and hollow. The hollow versions, open frames a reader can see straight through, were new: nobody had drawn them that way before. The hollow model in your hand keeps the same idea.

SourceLuca Pacioli, De divina proportione (Venice, 1509), plates by Leonardo da Vinci · MAA Convergence, “Mathematical Treasure: Luca Pacioli's Divina Proportione”

Ball-and-stick model of the methane molecule, CH4 (carbon black, hydrogen white), CRC bond lengths — Ben Mills (own work, computer-rendered — not AI) — 2009 — Wikimedia Commons — File:Methane-CRC-MW-3D-balls.png

Applications Today

Carbon's four bonds point at the corners of a tetrahedron, 109.47° apart. That one angle is why organic molecules are three-dimensional objects rather than flat diagrams — and why chemists build models rather than drawings.

SourceEncyclopaedia Britannica, “tetrahedral molecular geometry” · Royal Society of Chemistry — rsc.org

Two tetrahedra, one the dual of the other — Kepler, 1619

Did you know?

It is its own opposite

Join the centres of its four faces and you get another tetrahedron. It is the only solid that is its own dual.

One more thing

Every carbon atom in us sits at the centre of a tetrahedron, four bonds aimed at its corners — more of them in one body than stars in the visible universe.

SourceRoyal Society of Chemistry — rsc.org · European Space Agency — esa.int, “How many stars are there in the Universe?”

The simplest solid there is — and the one our bodies are built from.

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

Disc 1 and the three uprights 2 make a tripod; stand it on face 3.

4

THE THREE SIDES

Faces 4, 5, then 6 slot onto the uprights, engraved lines outward.

5

PAINT LAST

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

What it will not do

Not a precision die. It works as one — a little big for the table — and the small connectors keep it from lying perfectly flat. First 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