We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?
In this article, we look at solids constructed using symmetries of their faces.
In a recent workshop, students made these solids. Can you think of reasons why I might have grouped the solids in the way I have before taking the pictures?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
