Platonic solids

Construct and investigate 3d shapes

Key stage: 2
Subjects: mathematics, shapes, solids


  • Provide an introduction to classification of 3d shapes - what does it mean for a 3d shape to be regular? (same number and type of regular polygons meeting at every vertex)
  • Explore possible shapes that can be formed with only triangular, square or pentagonal faces
  • Use modelling equipment based on (1) faces and (2) vertices and edges to construct solids
  • To know about the names of the Platonic solids (including hexahedron as another name for the cube)
  • To explain why there are only 5 that can be made
  • To investigate Euler's formula relating numbers of edges, faces and vertices


Platonic solids are the set of regular 3d shapes. Unlike regular polygons, of which there can be an infinite number, the group of fully regular solids is small. In 3d, regularity entails all faces to be the same; all faces to be a regular polygon (resulting in all edges of the 3d shape being of equal length) and the same number of faces to meet at each vertex.

For this masterclass, pupils will need to construct 3d shapes from assembling faces and from assembling edges and vertices. The illustrations in the presentation show shapes made from Polydron and Zome, but there are a variety of other products and equipment that can be used to similar effect. Pupils could use cardboard shapes and sticky tape for assembling the shapes from faces and could use straws and plasticine for assembling shapes from edges.

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