Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.
This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?
The second in a series of articles on visualising and modelling shapes in the history of astronomy.

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.