Two things that roll

Toy 1 · A boat-shaped top

The stubborn top

A rattleback looks like a smooth wooden boat, curved underneath. Spin it one way and it spins happily. Spin it the other way and within a few turns it starts rocking end to end, stops, and spins back the way it likes. The trick is hidden inside: its weight is turned a few degrees off its long axis. Here, the blue line on the deck shows how the weight runs; the dashed line is the shape’s own axis.

Spin it right and in about 3 seconds the rocking takes over and turns the spin around. Spin it left and it holds for about 14 seconds before the same thing happens. Tap one end and the rocking turns into a spin, always to the left. Remove the twist (weight lined up with the shape) and none of this happens: it just keeps spinning whichever way you sent it.

What the model leaves out: real rattlebacks slide a little and lose energy in ways a simple drag only roughly copies. With no friction at all this model reverses both ways, just at very different speeds; a real one usually runs out of spin before the slow reversal arrives, which is why it seems to have only one bad direction.

Toy 2 · A game you can’t win

One way to lie still

Cut any flat shape out of card and stand it on its edge on a table. It can rest in some positions (green) and balance on a point in others (red). Can you make a shape with only one resting position? Drag the white dots to reshape it, click empty space to add a dot, or let the computer try thousands.

You can’t win. Every solid flat shape of even thickness has at least two ways to rest and two ways to balance. In three dimensions the rule breaks: a solid can have just one of each. The first one, the Gömböc, was found in 2006 and looks like a smooth, oddly pinched pebble. It always rights itself, like a turtle rolling onto its feet.

What the model leaves out: the shape is perfectly rigid and evenly heavy, and the floor is perfectly flat. Resting and balancing points are found on 2,880 sampled directions, so two points closer together than an eighth of a degree would count as one.

Prior art

Who got there first

The code behind every number runs in your browser: rattle-core.js (the rattleback’s equations of motion), rattle.js (drawing it), flat.js (resting points and the 3,000-shape search).

Next click down

The 2026 polyhedron is published as a list of flat cuts, so it can be built and rolled in a browser like the die. That’s the obvious next toy once the file is public.