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?

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?

Triangles to Tetrahedra

Age 11 to 14 Challenge Level:

Think about how the lengths of sides of the triangles are
important.

You could use Polydron (plastic shapes that click
together) to make the models yourself.