A decagon is a shape with 10 sides and 10 corners.
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Regular decagon
All sides of a regular decagon are the same length. Each corner is 144°. All corners added together equal 1440°.
Area
The amount of space a regular decagon takes up is
a is the length of one of its sides.
An alternative formula is where d is the distance between parallel sides, or the height when the decagon stands on one side as base.
By simple trigonometry .
Sides
The side of a regular decagon inscribed in a unit circle is , where ϕ is the golden ratio, .
Dissection of regular decagon
Coxeter states that every parallelsided 2mgon can be divided into m(m1)/2 rhombs. For the regular decagon, m=5, and it can be divided into 10 rhombs, with examples shown below. This decomposition can be seen as 10 of 80 faces in a Petrie polygon projection plane of the 5cube. A dissection is based on 10 of 30 faces of the rhombic triacontahedron. The list A006245 defines the number of solutions as 62, with 2 orientations for the first symmetric form, and 10 orientations for the other 6.
5cube 
Skew decagon
A skew decagon is a skew polygon with 10 vertices and edges but not existing on the same plane. The interior of such an decagon is not generally defined. A skew zigzag decagon has vertices alternating between two parallel planes.
A regular skew decagon is vertextransitive with equal edge lengths. In 3dimensions it will be a zigzag skew decagon and can be seen in the vertices and side edges of a pentagonal antiprism, pentagrammic antiprism, and pentagrammic crossedantiprism with the same D_{5d}, [2^{+},10] symmetry, order 20.
These can also be seen in these 4 convex polyhedra with icosahedral symmetry. The polygons on the perimeter of these projections are regular skew decagons.
Dodecahedron 
Icosahedron 
Icosidodecahedron 
Rhombic triacontahedron 
Related pages
 Decagonal number and centered decagonal number, figurate numbers modeled on the decagon
 Decagram, a star polygon with the same vertex positions as the regular decagon
 Eric W. Weisstein, Decagon at MathWorld.
