Regular Pentagons
In a regular pentagon, all sides are equal in length and each interior angle is 108°. A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). Its Schläfli symbol is {5}. The diagonals of a regular pentagon are in golden ratio to its sides.
The area of a regular convex pentagon with side length t is given by
A pentagram or pentangle is a regular star pentagon. Its Schläfli symbol is {5/2}. Its sides form the diagonals of a regular convex pentagon – in this arrangement the sides of the two pentagons are in the golden ratio.
When a regular pentagon is inscribed in a circle with radius R, its edge length t is given by the expression
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Famous quotes containing the word regular:
“While you’re playing cards with a regular guy or having a bite to eat with him, he seems a peaceable, good-humoured and not entirely dense person. But just begin a conversation with him about something inedible, politics or science, for instance, and he ends up in a deadend or starts in on such an obtuse and base philosophy that you can only wave your hand and leave.”
—Anton Pavlovich Chekhov (1860–1904)