Sunday Times Teaser 2762 – What a Gem!
by Michael Fletcher
Published: 30 August 2015 (link)
A friend showed me a beautiful gem with shiny flat faces and lots of planes of symmetry. After a quick examination I was able to declare that it was “perfectly square”. This puzzled my friend because none of the faces had four edges. So I explained by pointing out that the gem’s number of faces was a perfect square, its number of edges was a perfect square, and its number of vertices was a perfect square.
How many faces did it have, and how many of those were triangular?