The *angle defect* at a vertex of a polygon is defined to be
minus the sum of the angles at the corners of the faces at that vertex.
For instance, at any vertex of a cube there are three angles of ,
so the angle defect is . You can visualize the angle defect by
cutting along an edge at that vertex, and then flattening out a neighborhood
of the vertex into the plane. A little gap will form where the slit is:
the angle by which it opens up is the angle defect.

The *total angle defect* of the polyhedron is gotten by adding up the
angle defects at all the vertices of the polyhedron. For a cube,
the total angle defect is .

- What is the angle sum for a polygon (in the plane) with sides?
- Determine the total angle defect for each of the 5 regular polyhedra, and for the polyhedra handed out.