3D Shapes

The idea, step by step

Start here. A 3D shape is called a solid. A dice is a cube, a ball is a sphere, a tin can is a cylinder and a party hat is a cone. Some solids have flat sides and some have a curved surface.

Faces, edges and corners. A face is a flat side. An edge is where two faces meet. A corner (also called a vertex) is where edges meet. A cube has 6 faces, 12 edges and 8 corners. In this game a curved surface counts as 1 face, a circle where a flat face meets a curved face counts as 1 edge, and the pointy tip of a cone counts as 1 corner.

A rule that always works. For solids with only flat faces, corners − edges + faces = 2. Check it on a cube: 8 − 12 + 6 = 2. It is called Euler's rule (say "oiler"). If you know two of the numbers you can find the third.

Prisms. A prism has the same shape at both ends and flat rectangles joining them. If the end shape has n sides, the prism has n + 2 faces, 3n edges and 2n corners. A triangular prism: 5 faces, 9 edges, 6 corners.

Nets. A net is a solid unfolded flat. A cube has 11 different nets, but most ways of joining six squares do not fold into a cube, because two squares land on the same face and one face is left open.

Try this above. In the workshop, pick the cube and press "Count one by one" for faces. Then pick the triangular prism and press "Unfold". Finally try the Net Puzzles and see which six squares really fold.

Questions