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We have some confusion about the language to use with 3D shapes, can you help?

Spheres are often referred to having one face, cones two faces and cylinders three faces. Mathematically a face on a 3D shape is part of a plane and therefore is flat. Does this means that much of the language that has been used in inaccurate?
We have had a discussion about explaining that a sphere has a curved surface; a cone has 1 face and 1 curved surface etc. However, the definition of an edge is that it is where 2 faces meet. How does this become explained? Have you any suggestions?


Great question! I'm asked quite a lot about this when running courses. I remember when writing a maths dictionary many years ago that it was a point of contention between maths academics at the time. Some of the issues are because we want it defined for primary school use to make it accessible to our children.

It is best to consider this by sorting shapes by their properties. Start with any 3D or solid shape and they can be classified as polyhedra and non-polyhedra.


A polyhedron is any solid shape which has faces that are polygons, joined at their edges to make a solid. As a polygon is a closed shape made with straight sides, the edges of a polyhedron are therefore straight, with plane faces, not curved. You could then further classify and sort the shapes in this set - cubes, cuboids, pyramids, prisms, platonic solids etc. The relationship between the vertices, edges and faces (Euler's Formula) is only valid for different polyhedra.

Now we can look at the other set of non-polyhedra, and these will include spheres, cones, cylinders and hemispheres. As these are not made with faces of polyhedra, then they include curved surfaces, faces and curved edges. This is where definitions get a little loose at primary level, but if you are consistent and make a clear distinction between surfaces and faces as well as edges and curved edges then this should be fine. 
You are just about spot on with your thoughts on this in your discussion:
   • a sphere has a single curved surface and no edges or vertices.
   • a cone has one curved surface, a flat face with a curved edge (usually, but not always, a circle) and    
   an apex. To make it clearer, the face can be called a base and the point is the apex, not a vertex.

   • a cylinder has one curved surface, two curved edges (always circles) and no vertices.
   • a hemisphere has one curved surface, a flat face and a curved edge (always a circle).
Hope that helps.
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