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A skew decagon is a skew polygon with 10 vertices and edges but not existing on the same plane. The interior of such a decagon is not generally defined. A skew zig-zag decagon has vertices alternating between two parallel planes. A regular skew decagon is vertex-transitive with equal edge lengths.
A regular decagram is a 10-sided polygram, represented by symbol {10/n}, containing the same vertices as regular decagon.Only one of these polygrams, {10/3} (connecting every third point), forms a regular star polygon, but there are also three ten-vertex polygrams which can be interpreted as regular compounds:
Golden triangles can also be found in a regular decagon, an equiangular and equilateral ten-sided polygon, by connecting any two adjacent vertices to the center. This is because: 180(10−2)/10 = 144° is the interior angle, and bisecting it through the vertex to the center: 144/2 = 72°. [1]
A pentagon is a five-sided polygon. 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.
Square (regular quadrilateral) Tangential quadrilateral; Trapezoid. Isosceles trapezoid; Trapezus; Pentagon – 5 sides; Hexagon – 6 sides Lemoine hexagon; Heptagon – 7 sides; Octagon – 8 sides; Nonagon – 9 sides; Decagon – 10 sides; Hendecagon – 11 sides; Dodecagon – 12 sides; Tridecagon – 13 sides; Tetradecagon – 14 sides ...
For a regular n-gon, the sum of the perpendicular distances from any interior point to the n sides is n times the apothem [4]: p. 72 (the apothem being the distance from the center to any side). This is a generalization of Viviani's theorem for the n = 3 case.
A regular triangle, decagon, and pentadecagon can completely fill a plane vertex. However, due to the triangle's odd number of sides, the figures cannot alternate around the triangle, so the vertex cannot produce a semiregular tiling .
The regular icosagon has Schläfli symbol {20}, and can also be constructed as a truncated decagon, t{10}, or a twice-truncated pentagon, tt{5}. One interior angle in a regular icosagon is 162°, meaning that one exterior angle would be 18°. The area of a regular icosagon with edge length t is