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Here is a lesson I have created for a mixed/high ability year 7 group on Euler's formula for polyhedra. I have seen many lessons on this, but not as many go as in depth as I would have liked, as such ...

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The highlight of the 13th and final book of Euclid's Elements was the proof that there are just five "Platonic solids". Recall that a regular polygon is a plane figure with all sides and angles equal, ...

A 3D shape with all straight edges and flat faces is a polyhedron. Other 3D shapes with least one curved surface are not polyhedra. A 3D shape with regular polygonal faces, meeting at equal angles, is ...