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
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?
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