3D Objects

3D objects have 3 dimensions - length, width and height.

They are what we consider solids.

All 3D objects have surfaces that are curved, flat or a combination of both.

Faces are the flat surfaces of 3D objects that meet at edges.

Edges are where two planes (or faces) meet.

Vertices are where three or more edges meet.

Curved surfaces are rounded, not flat.

A cylinder, for example has a curved surface.

This is not a face.

A polyhedron is a 3D object or solid with many flat faces. Poly is Ancient Greek meaning many, hedra meaning face. So a polyhedron is a many-faced object. Looking at the Latin, Greek and Arabic roots of mathematical words is a good way to promote transference of understanding.

A regular polyhedron has faces that are identical regular polygons (see 2D Shapes) and all the faces meet at the same angle.

There are only five regular polyhedra (polyhedrons). These are know as the Platonic solids, named after the Athenian philosopher Plato. Looking at the history of these solids is fascinating, particularly their association with the four basic elements of fire, air, water, earth and later the constellations.

Prisms

A prism is a 3D object or solid. Prisms have all flat surfaces and their faces are polygons.

Polygons are 2D shapes with straight sides (see 2D Shapes).

Prisms have two parallel faces that are identical in size and shape and rectangular lateral faces that join them. The parallel faces are polygons that give the prism its name.

For example, the triangular prism in the table below has a triangular top face and bottom face that are parallel, and the same size and shape. All the other faces are rectangular.

A tricky one for many people is the cylinder. Is it a prism?

It has a top face and a bottom face (or parallel ends) that are the same size and same shape... but they are circular therefore they don't have straight sides, and cannot be a polygon.

The cylinder has a curved surface joining the ends (or curved boundary) but no faces.