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
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.
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.
What are the limitations on the lengths of the sides of any triangle?
Look at different cases.
If the base is a 4 by 5 by 6 triangle, what size can the other faces be?
How many different tetrahedra can have as its base a 4 by 5 by 6
Can you find 8 or more possible tetrahedra?
How will you know when you have them all?