General Properties
These properties apply to all regular polygons, whether convex or star.
A regular n-sided polygon has rotational symmetry of order n.
All vertices of a regular polygon lie on a common circle (the circumscribed circle), i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon.
Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus a regular polygon is a tangential polygon.
A regular n-sided polygon can be constructed with compass and straightedge if and only if the odd prime factors of n are distinct Fermat primes. See constructible polygon.
Read more about this topic: Regular Polygon
Famous quotes containing the words general and/or properties:
“Mr. Chadband is a large yellow man, with a fat smile, and a general appearance of having a good deal of train oil in his system.”
—Charles Dickens (1812–1870)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)