Or if one extends the sides until the non-adjacent sides meet, one obtains a larger pentagram. The sum of the internal angles in a simple pentagon is 540°. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.

A regular pentagon has Schläfli symbol and interior angles are 108°.

The area of a cyclic pentagon, whether regular or not, can be expressed as one fourth the square root of one of the roots of a septic equation whose coefficients are functions of the sides of the pentagon.

There exist cyclic pentagons with rational sides and rational area; these are called Robbins pentagons.

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 sides.A cyclic pentagon is one for which a circle called the circumcircle goes through all five vertices.The regular pentagon is an example of a cyclic pentagon.To determine the length of this side, the two right triangles DCM and QCM are depicted below the circle.Using Pythagoras' theorem and two sides, the hypotenuse of the larger triangle is found as 7a. It intersects the original circle at two of the vertices of the pentagon.Only the g5 subgroup has no degrees of freedom but can seen as directed edges.

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