Pentagon Pentagon In geometry, a pentagon (from the Greek πέντε "pente" and γωνία "gonia", meaning "five" and "angle") is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting "regular pentagon" (or "star pentagon") is called a pentagram. A "regular pentagon" has Schläfli symbol {5} and interior angles are 108°. A "regular pentagon" has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its
The Pentagon was planned accordingly as an irregular pentagon. Concerned that the new building could obstruct the view of Washington, D.C., from Arlington Cemetery, President Roosevelt ended up selecting the Hoover Airport site instead. The building retained its pentagonal layout because a major redesign at that stage would have been costly, and Roosevelt liked the design. Freed of the constraints of the asymmetric Arlington Farms site, it was modified into a regular pentagon which resembled the fortifications of the gunpowder age. On July 28, Congress authorized funding for a new Department of War building in Arlington, which would house the entire department