Almost everyone knows that the inner angles of a triangle sum to 180o. But if you ask the typical mathematician how to sum the solid inner angles over the vertices of a tetrahedron, you are likely to receive a blank stare or a mystified shrug. In some cases you may be directed to the Gram-Euler relations for higher dimensional polytopes [3, 4, 6, 7], a 19th century result unjustly consigned to ...