  Every polygon $P$ can be companioned by a cap polygon $\hat P$ such that $P$
and $\hat P$ serve as two parts of the boundary surface of a polyhedron $V$.
Pairs of vertices on $P$ and $\hat P$ are identified successively to become
vertices of $V$. In this paper, we study the cap construction that asserts
equal angular defects at these pairings. We exhibit a linear relation that
arises from the cap construction algorithm, which in turn demonstrates an
abundance of polygons that satisfy the closed cap condition, that is, those
that can successfully undergo the cap construction process.
