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A tetrahedron has 4 vertices, 6 edges and 4 faces. Can you number them 1 to 14 in such a way that the number on each edge is the mean of the two numbers at the vertices joined by that edge and also the mean of the two numbers on the faces it separates?
Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?