Math & words · Science

A Donut Is a Torus

A runaway 3D printer makes geometry delicious.

Watch on YouTube
A Donut Is a Torus3:17

A song. A few new discoveries.

  • Name spheres, cubes, cylinders, cones, prisms, pyramids, and a torus.
  • Meet the five Platonic solids and compare their faces.
  • Explore faces + vertices − edges = 2 for convex polyhedra, such as a cube. That rule does not apply unchanged to a torus.

Keep the curiosity going

Which 3D shapes can you find in your kitchen?

Made for curious kids around ages 6–12 and the grown-ups watching with them. Music and animation created with AI tools under Mike Sego’s direction. YouTube’s video description includes the release notes and credits.

Read the sing-along lyrics
Smarty Party! I built a 3-D printer. It can print any shape. Any shape at all. ...Let's test it! A sphere is a ball, like a marble or the Moon— Round every way, like a big balloon. A cube has six faces, all squares, like dice; A cylinder's a can, and a cone's ice cream—nice! A pyramid points up with a square at the base; A triangle prism's like a tent in a sunny place; A hexagon prism's like a pencil, long and thin— Or a honeycomb cell with the honey poured in! Faces, edges, corners, too— Every shape's got a shape for you! Round and flat and pointy, wow— Print it, print it, print it now! And what's a donut? It's a torus! What's a donut? It's a torus! Now here come the perfect dice, the fairest you can find: Every face and every corner match—just five of this kind! Four triangles make a tetrahedron, sharp and small; Six squares make a cube, you've seen it all; Eight triangles? Octahedron—watch it shine! Twelve pentagons: a dodecahedron—so fine! Twenty triangles: the icosahedron, rolling far— The only five perfect dice—and there they are! Faces, edges, corners, too— Every shape's got a shape for you! Round and flat and pointy, wow— Print it, print it, print it now! And what's a donut? It's a torus! What's a donut? It's a torus! Here's a secret trick that the mathematicians knew: Take the faces and the corners, then subtract the edges, too. On a cube: six plus eight, take twelve away... It's two! It's always two, on shapes like these, hooray! A cone, a cube, a sphere, a pyramid, a prism, whoa! The printer's printing faster and it's printing more, you know! Dodecahedron, icosahedron, one more try— It printed a donut! It's a torus! My, oh my! Faces, edges, corners, too— Every shape's got a shape for you! Round and flat and pointy, wow— Print it, print it, print it now! And what's a donut? It's a torus! What's a donut? It's a torus! I love geometry. It's delicious. Smarty Party Songs! Like, subscribe, PARTY!

Lyrics from the published video’s caption file.

Keep the discoveries coming.

For the grown-ups

Keep the discoveries
coming.

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