Faces, corners and edges

In your book, Maths Mela (Chapter 1), you build solids with straws and small balls of clay. Each straw is an edge, where two faces meet. Each clay ball is a corner, where edges meet. The flat sides are the faces. We write F for faces, V for corners and E for edges.

Count them for each solid. A cube has 6 faces, 8 corners and 12 edges. A cuboid has the same: 6 faces, 8 corners, 12 edges. A triangular pyramid has 4 faces, 4 corners and 6 edges. A square pyramid has 5 faces, 5 corners and 8 edges. A triangular prism has 5 faces, 6 corners and 9 edges.

Now add the faces and the corners, and take away the edges: F + V − E. For the cube, 6 + 8 − 12 = 2. For the triangular pyramid, 4 + 4 − 6 = 2. For the square pyramid, 5 + 5 − 8 = 2. For the triangular prism, 5 + 6 − 9 = 2. We get 2 every time!

Straws and clay balls can also tell you which solid a model is. 12 straws of the same length and 8 clay balls make a cube. 9 straws and 6 balls make a triangular prism: 3 edges round each triangle end and 3 joining them. 10 straws and 6 balls make a pentagonal pyramid: 5 straws round the pentagon base, 5 going up to the top, and 5 corners on the base plus 1 at the top.