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Proximity

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Platonic Planet

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

Three Cubes

Can you work out the dimensions of the three cubes?

Sliced

Age 14 to 16
Challenge Level

Image of tetrahedron with sides of length

An irregular tetrahedron has two opposite sides the same length ($a$ say) and the line joining their midpoints is perpendicular to these two edges and is of length $b$. What is the volume of the tetrahedron?



The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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