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: • {10/5} is a compound of five degenerate
digons 5{2} • {10/4} is a compound of two
pentagrams 2{5/2} • {10/2} is a compound of two
pentagons 2{5}. {10/2} can be seen as the 2D equivalent of the 3D
compound of dodecahedron and icosahedron and 4D
compound of 120-cell and 600-cell; that is, the compound of two
pentagonal polytopes in their respective dual positions. {10/4} can be seen as the two-dimensional equivalent of the three-dimensional
compound of small stellated dodecahedron and great dodecahedron or
compound of great icosahedron and great stellated dodecahedron through similar reasons. It has six four-dimensional analogues, with two of these being compounds of two self-dual star polytopes, like the pentagram itself; the
compound of two great 120-cells and the
compound of two grand stellated 120-cells. A full list can be seen at Polytope compound#Compounds with duals. Deeper truncations of the regular pentagon and pentagram can produce intermediate star polygon forms with ten equally spaced vertices and two edge lengths that remain
vertex-transitive (any two vertices can be transformed into each other by a symmetry of the figure). ==See also==