3:06Math & words · Science
A Donut Is a Torus
A runaway 3D printer makes geometry delicious.
Watch on YouTube
3:17A 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!
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PARTY!
Lyrics from the published video’s caption file.
Keep the discoveries coming.
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