3D Shape Builder

Pre-Algebra · Axiom Academy

A flat pattern and a solid block are the same object — one folded, one flat. Watch a net fold up, then fold a few yourself. A flat pattern is a solid waiting to fold Cut a cereal box along its edges and flatten it: you get a flat pattern called a net . Run it backwards and the flat pattern stands up into a solid. Every box, can, and pyramid you'll ever meet is built this way, so it pays to see the two as one thing — and the cleanest way to believe it is to watch it happen. Here is the net of a cube: six squares joined edge to edge in a cross. Press play and watch the four side squares swing up along their creases while the last square drops on as a lid. Each crease in the flat pattern becomes an edge of the solid. Six flat squares, six creases, and you have a cube — surface still made of the exact same six pieces. Different nets, different solids The cube isn't special — every solid has its own net. Pick a shape, then drag the slider to fold its flat net all the way up. Watch the counts on the right: the number of flat pieces in the net is exactly the number of faces on the finished solid. Square pyramid: 1 square + 4 triangles. Triangular prism: 2 triangles + 3 rectangles. Count the net, and you've counted the faces. Go the other direction. Drag to peel a closed cube back into its flat net, and a piece lifts off one at a time. Each piece is one face of the solid — so counting the pieces of any net tells you how many flat surfaces the solid has, before you ever fold it.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.