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4. Three-dimensional objects

Regular three-dimensional (3-D) objects are commonly analogues of two-dimensional objects. Instead of being delimited by one-dimensional lines, they are defined by flat or curved planes. In the case of spheres (3-D analogue of a circle) and ellipsoids (3-D analogues of ellipses), a single and continuous curved plane delimits the object. Other 3-D objects have edges where planes meet. The family of cuboids are delimited by six planes, opposite pairs of which are parallel, and have straight edges.

A variety of 3-D objects collectively known as prisms have identically-shaped planes at their ends and the long sides made up of one or more planes forming a parallel-sided 'tube'. A cylinder is a prism with circular ends.

There is a corresponding family of tapered objects, where the base is a flat plane but the long sides are not parallel and the 'top' is a point. Such an object with a circular base is a cone, whilst a pyramid can have a triangular or quadrilateral base. A pyramid made up from four equilateral triangles is called a tetrahedron.

3-D objects delimited completely by polygons – polyhedra - are more complex. Many natural and man-made structures can be represented in this way – examples include virus capsids, footballs and geodesic domes.

As with 2-D objects, the area of 3-D objects is related to the square of linear dimension(s). Volume is a measure of the space that the object occupies in three dimensions, and is a function of the cube of the linear dimension(s).