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Reach for Polydron

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

Tetra Inequalities

Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.

The Dodecahedron Explained

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

Tetra Perp

Age 16 to 18
Challenge Level

Why do this problem?
A well known result but nevertheless a good exercise in using vectors including the scalar product.

Key question
How do you write down what is given in the question in terms of vectors?