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A Chain of Eight Polyhedra

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

These two 3-D shapes, the tetrahedron and the octahedron have the same 2-D shape, an equilateral triangle, as their faces.

Tetrahedron equilateral triangle and octahedron

Can you arrange the shapes below in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it? (The faces do not have to be the same size.)

eight polyhedra: cube, pentagonal based pyramid, pentagonal prism, square based prism, hexagonal prism, cuboid, hexagonal based prism, triangular prism


How many ways can you find to make a loop (a closed chain) using all the shapes so that each one shares a face (or faces) that are the same shape as the one that follows it?