An alternative formula is whered is the distance between parallel sides, or the height when the decagon stands on one side as base. By simple trigonometry.
Coxeter states that every parallel-sided 2m-gon can be divided intom(m-1)/2 rhombs. For theregular 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 aPetrie polygon projection plane of the5-cube. A dissection is based on 10 of 30 faces of therhombic triacontahedron.[1] The listA006245 defines the number of solutions as 62, with 2 orientations for the first symmetric form, and 10 orientations for the other 6.
Askew decagon is askew polygon with 10 vertices and edges but not existing on the same plane. The interior of such an decagon is not generally defined. Askew zig-zag decagon has vertices alternating between two parallel planes.
These can also be seen in these 4 convex polyhedra withicosahedral symmetry. The polygons on the perimeter of these projections are regular skew decagons.
Orthogonal projections of polyhedra on 5-fold axes
