Free learning resources from arts, cultural and heritage organisations.

How Many Dimensions are there?

A dot has no dimensions – it has no length, width, or depth. If you were to draw another dot and connect them with a line, this would have one dimension.  If you were to then connect three lines to make a triangle shape, this would have two dimensions – it would be a flat shape, ‘two dimensional’ as it has length and width. In maths, we call these two dimensional shapes polygons.  A triangle, circle, square or rectangle are all two-dimensional shapes.   We use dots, lines and shapes as the basis of art and design.


A fully white room with large bay windows overlooking a garden and fence. The ceiling of the window is decorative paneling with coving features. Small metal white radiators are below three of the windows. Through one window there are sculptures of tubes and balls shapes within buses and trees.
Gemma Anderson-Tempini, And She Built a Crooked House, 2023

If you add depth to a two-dimensional shape you add another dimension – so it becomes a three-dimensional shape.   Adding depth to a square makes it a cube, and a cube is three-dimensional.    If you add depth, you also create volume – which is the space inside the shape.   Three dimensional shapes with flat sides (like cubes and pyramids) are called polytopes.

A metal sculpture sits on a wooden floor with light emanating from within.The sculpture is made of many pieces of metallic pieces on a small stand at floor height. Casting shadows onto white walls.
Gemma Anderson-Tempini, And She Built a Crooked House, 2023

We live in a three-dimensional world.  Things we can touch and hold are three-dimensional. 

We can only imagine the fourth dimension, but Mathematicians and physicists are exploring this more all the time. 

An example of a four-dimensional shape would be a cube within a cube – also known as a tesseract. 

The exhibition “And She Built a Crooked House” explored the fourth spatial dimension in art - watch the YouTube video in which artist explains her artwork (see Supporting Links).

You can also make your own exploded fourth-dimensional shape using the activity sheet here!