Vault

Let a vault consist of two equal half-Cylinders of length and diameter $2a$ which intersect at Right Angles so that the lines of their intersections (the ``groins'') terminate in the Vertices of a Square. Then the Surface Area of the vault is given by

$$A=4(\pi-2)a^2.$$

See also Dome

References

Lines, L. Solid Geometry. New York: Dover, pp. 112-113, 1965.