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  2. Pentagon - Wikipedia

    en.wikipedia.org/wiki/Pentagon

    A regular pentagon has Schläfli symbol {5} and interior angles of 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 sides.

  3. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...

  4. Equilateral pentagon - Wikipedia

    en.wikipedia.org/wiki/Equilateral_pentagon

    In geometry, an equilateral pentagon is a polygon in the Euclidean plane with five sides of equal length. Its five vertex angles can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal ...

  5. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    As n approaches infinity, the internal angle approaches 180 degrees. For a regular polygon with 10,000 sides (a myriagon) the internal angle is 179.964°. As the number of sides increases, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle.

  6. List of polygons - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons

    A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular ...

  7. Polygon - Wikipedia

    en.wikipedia.org/wiki/Polygon

    Exterior angle – The exterior angle is the supplementary angle to the interior angle. Tracing around a convex n -gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full turn , so the sum of the exterior angles must be 360°.

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  9. Table of polyhedron dihedral angles - Wikipedia

    en.wikipedia.org/wiki/Table_of_polyhedron...

    exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex) Tetrahedron {3,3} (3.3.3) arccos (⁠ 1 / 3 ⁠) 70.529° Hexahedron or Cube {4,3} (4.4.4) arccos (0) = ⁠ π / 2 ⁠ 90° Octahedron {3,4} (3.3.3.3) arccos (-⁠ 1 / 3 ⁠) 109.471° Dodecahedron {5,3} (5.5.5) arccos ...

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