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A Mean Tetrahedron

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

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Tetra Square

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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Triangles to Tetrahedra

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Icosian Game

Stage: 3 Challenge Level: Challenge Level:1

Use symmetry and similar triangles