Solids and the Euler Characteristic
Choose your solid by clicking New Shape. You can view each solid and rotate it in space by clicking and dragging the mouse.
To facilitate the counting of vertices, edges, and faces, each can be marked. Hold down the Shift key and click on a face (or edge or vertex). When you shift-click, a face changes color, an edge turns white, and a vertex is marked with a black dot.
As you mark faces, vertices, and edges, there is a running tally in the box. When you have marked every part of your solid, the Euler characteristic, V - E + F, is computed.