Suppose we draw a square on a piece of paper. Can we select 3 of the given square's vertices to be the vertices of a regular triangle? No! What if we ask the analogous question in R^3 - can we select 4 vertices of a cube such that they form the vertices of a regular tetrahedron? Yes! Why could we do this in 3D but not in 2D, and can we do this in other dimensions? We will explore this discrete geometric question in higher dimensions and show its applications in other areas of maths. The talk should be very elementary and require no serious background knowledge in any particular area.