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
Pentagon if one joins the non-adjacent corners (drawing the diagonals of the pentagon), one obtains a pentagram, with a smaller regular pentagon in the center. Or if one extends the sides until the non-adjacent sides meet, one obtains a larger pentagram. The accuracy of this method depends on the accuracy of the protractor used to measure the angles. The "regular pentagon" has Dih symmetry, order 10. Since 5 is a prime number there is one subgroup with dihedral symmetry: Dih, and 2 cyclic group symmetries: Z, and Z. These 4 symmetries can be seen in 4 distinct symmetries on the pentagon.