MathDB

A cuboctahedron is the convex hull of (smallest convex set containing) the

12

points

(\pm 1, \pm 1, 0), (\pm 1, 0, \pm 1), (0, \pm 1, \pm 1)

. Find the cosine of the solid angle of one of the triangular faces, as viewed from the origin. (Take a figure and consider the set of points on the unit sphere centered on the origin such that the ray from the origin through the point intersects the figure. The area of that set is the solid angle of the figure as viewed from the origin.)

Problem Statement