DA VINCI OCTAHEDRON d8 — 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_AV0118103.pdf — 198 × 298 mm, EN/FR

Learn

Four ways in

Octaedron planum vacuum — hollow octahedron, woodcut after Leonardo's drawing, plate XVI 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 n220 — divinaproportion00paci, page n220

A Timeless History

In the Timaeus the octahedron is air — lighter than earth, heavier than fire, and loose enough to be turned in the fingers. Euclid built the five solids in order in Book XIII of the Elements and finished by proving no sixth is possible — one of the oldest complete proofs in mathematics. In 1509 Leonardo drew it for Pacioli as an open frame, edges only: the way this model is built.

SourcePlato, Timaeus (c. 360 BC) · Encyclopaedia Britannica — britannica.com · Euclid, Elements, Book XIII · Mathematical Association of America, Convergence — maa.org · Luca Pacioli, De divina proportione, Venice 1509, plate XVI

Octahedron with its inscribed tetrahedra, and the octahedron inscribed in the cube — woodcuts on p. 181 of Harmonices Mundi, Book V, chapter 1 (De quinque figuris solidis regularibus) — Johannes Kepler — 1619 — Wikimedia Commons scan of the Smithsonian Libraries copy on the Internet Archive (ioanniskepplerih00kepl) — File:Ioanniskepplerih00kepl 0271.jpg

Science In Action

Six vertices, twelve edges, eight triangular faces: 6 − 12 + 8 = 2, Euler's rule, true for all five solids • Dual of the cube — six faces and eight corners against eight faces and six corners, exactly swapped • Two pyramids — cut it across the middle and you hold two square-based pyramids, base to base • Kepler drew it inside a cube in 1619, its six points touching the six faces — duality on the page

SourceEncyclopaedia Britannica, “polyhedron” · Wolfram MathWorld, “Octahedron” — mathworld.wolfram.com · Johannes Kepler, Harmonices Mundi, Book V (Linz, 1619)

The octahedron filled with air (birds and clouds) — 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 cut woodblocks of all five solids for the Harmonices Mundi in 1619 and filled each with its element — birds and clouds in the octahedron, fish and waves in the icosahedron, flames in the tetrahedron. Four hundred years on they remain the clearest picture of Plato's idea: a shape that is not just a shape, but a piece of the world.

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

Fluorite, octahedral green crystals — north of Riemvasmaak, Northern Cape Province, South Africa (museum specimen) — James St. John (Flickr jsjgeology) — 2015 — Wikimedia Commons — File:Fluorite (north of Riemvasmaak, Northern Cape Province, South Africa) 1.jpg

Applications Today

Fluorite and diamond both crystallise as octahedra, and the geometry is not decorative: diamond cleaves along those octahedral planes, which is how a cutter splits a stone with one controlled tap instead of a saw.

SourceSmithsonian National Museum of Natural History — naturalhistory.si.edu · Encyclopaedia Britannica, “diamond”

A rough diamond, grown as an octahedron — Venezuela

Did you know?

Diamonds come out of the ground this way

Rough diamond often grows as a natural octahedron. The cutter's first job is deciding how much of that shape to destroy.

One more thing

A diamond cutter splits a rough stone along its octahedral planes — the same faces you are holding. Get the angle wrong and the stone shatters instead.

SourceEncyclopaedia Britannica, “diamond”

Plato called it air. The earth has been growing it in diamond for three billion years.

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 FRAME

Four fins into the base plate, turn it over, four more: the frame.

4

THE EIGHT FACES

Faces go on top first (6, 7, 2, 3), then below (4, 1, 8, 5).

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