A cube has exactly 11 distinct nets. There are 35 ways to join six squares edge to edge, but only 11 of them fold up into a cube, counting shapes that match after a rotation or a flip as the same net. On this page all 11 open out one at a time from the solid, and once the full set is on screen the sequence starts again.
The faces are colour-coded, and the display panel can also print a number on each one. A colour is decided by which face lands on the bottom as the cube rolls to the next square, so every net shows all six colours exactly once and you can see which colours end up opposite each other. The nets group by the length of their central strip: six are 1-4-1, a strip of four with one square on each side; three are 2-3-1; and the staircase 2-2-2 and the 3-3 make one each.
Use the shape panel to switch to a regular tetrahedron or a regular octahedron. The tetrahedron has two nets; the octahedron has eleven, the same count as the cube. They match because the cube and the octahedron are duals, so their faces join up in the same pattern. The angle a net folds back through differs for each solid: 90 degrees for the cube, about 109.47 for the tetrahedron and about 70.53 for the octahedron, each one the supplement of that solid's dihedral angle.
A cylinder and a cone are on the list as well. The cylinder net is a rectangle as wide as the base circumference and as tall as the cylinder, with a circle touching it at the top and another at the bottom. The cone net is a sector and a circle, and the central angle of the sector is 2π times the base radius divided by the slant height, so a radius exactly half the slant gives a semicircle. The curved sides are not flat, so they are cut into thin strips and wedges and rolled up a little at a time. The display panel changes how fast the nets open.