3D geometry: total angle sum

if you sum all the angles of all the faces this is called the total angle sum (the TAS)
it was explored by Descartes (who obtained Euler's rule for polyhedra (V + F = E + 2) quite a bit before Euler)

this exploration was suggested to me by Gordon Haigh when he was at Wolverhampton University
it can be a good task to work on following a consideration of (interior) angles in regular polygons

the relationship is quite easily established (proved) for any prism and any pyramid

powerpoint: total angle sum