A Timeless History
Plato assigned the cube to earth in the Timaeus: the most stable of the five, the one that rests on a face and stays put. Euclid proved in Book XIII of the Elements that only five such solids can exist. The cube is the one every other culture found independently too — it is the shape of the brick, the die and the room we sit in. Roman Egypt was already rolling ivory ones.
SourcePlato, Timaeus (c. 360 BC) · Encyclopaedia Britannica — britannica.com · Euclid, Elements, Book XIII · Mathematical Association of America, Convergence — maa.org · The Metropolitan Museum of Art, die 97.4.119
Science In Action
Eight vertices, twelve edges, six square faces: 8 − 12 + 6 = 2, Euler's rule, true for all five solids • Dual of the octahedron — join the centres of its six faces and you get one; do it again and the cube is back • Space-filling — the only Platonic solid that stacks with no gaps, which is why bricks and containers are cubes • Three faces meet at every corner at 90° — the only regular solid whose faces meet at right angles
SourceEncyclopaedia Britannica, “polyhedron” · Euclid, Elements, Book XIII · Wolfram MathWorld, “Cube” — mathworld.wolfram.com
Arts
Renaissance woodworkers were drawing polyhedra in inlaid wood before Leonardo drew them on paper. The Gubbio studiolo of about 1478, now rebuilt inside the Metropolitan Museum, is panelled in intarsia — geometric solids rendered in cut and fitted wood, down to a faceted ring called a mazzocchio built from dozens of tiny quadrilaterals. The technique this model uses is 550 years old.
SourceThe Metropolitan Museum of Art — metmuseum.org, Studiolo from the Ducal Palace in Gubbio, c. 1478–82, acc. 39.153
Applications Today
Salt, pyrite and galena all crystallise as cubes because their atoms stack in a cubic lattice. Crystallographers read a mineral's internal structure from the shape it grows into — the outside is a report on the inside.
SourceSmithsonian National Museum of Natural History — naturalhistory.si.edu · Encyclopaedia Britannica, “crystal”
The most ordinary shape in the world turns out to be one of only five of its kind.
Die (ivory, six faces marked with ring-and-dot pips), Roman Period, Egypt — Unknown maker, Egypt — 30 BCE–330 CE — The Metropolitan Museum of Art, Egyptian Art — 97.4.119 (Gift of Egypt Exploration Fund, 1897)
