Classifying three-dimensional shapes

Three-dimensional shapes - part 2

These and other solid shapes can be constructed by drawing a two-dimensional net, such as those shown for the regular tetrahedron or cube, cutting these out, folding and sticking. It is advisable to incorporate some flaps for gluing in appropriate positions before cutting out.

A prism is a shape made up of two identical polygons at opposite ends, joined up by parallel lines. Examples include (a) a triangular prism, (b) a rectangular prism and (c) a hexagonal prism. I like to think of prisms as being made from cheese: a polyhedron is a prism if you can slice the cheese along its length in a way in which each slice is identical. Note that they are all called prisms, although colloquially the word is often used to refer to the triangular prism. Note also that another name for a rectangular prism is a cuboid: this is a three- dimensional shape in which all the faces are rectangles. A cube is, of course, a special kind of cuboid in which all the faces are squares. Note further that some ‘sugar cubes’ are cuboids but not cubes!

Another category of three-dimensional shapes to be mentioned here is the set called pyramids. A pyramid is made up of a polygon forming the base, and then lines drawn from each of the vertices of this polygon to some point above, called the apex. The result of this is to form a series of triangular faces rising up from the edges of the base, meeting at the apex. Note that (a) a triangular-based pyramid is actually a tetrahedron by another name, and that (b) a square-based pyramid is the kind we associate with ancient Egypt.