Faces, Edges and Vertices

Until now every shape lay flat on the page. A solid takes up space: it has length, width and height. The simplest one is a box, which geometry calls a cuboid.

A cuboid has 6 flat faces, all rectangles. Two faces meet along an edge, and there are 12 edges. Edges meet at corners called vertices, and there are 8. The hidden edges at the back are drawn dashed, so you can see the whole solid at once.

Three edges leave every corner, and they give the three measures of the box. In the figure the edge along the bottom front is the length, 6. The upright edge is the height, 2, and the edge going back into the page is the width, also called the depth, 3. Every other edge is a copy of one of these.