Enigma 1376: Square facts and faces
3 November 2013
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From New Scientist #2536, 28th January 2006
I have just constructed a simple polyhedron, i.e. a three-dimensional solid figure with some vertices, straight edges, and faces. The number of vertices is a square; the number of edges is a square; the number of faces is a square; the total number of vertices and edges is a square; and over half of the faces are squares! How many faces are there, and how many of those are triangles?