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Regular version of the site

Working paper

Polygons in three-dimensional space

math. arxiv. Cornell University, 2020
Let P=A_1...A_n be a generic polygon in three-dimensional space and let v_1,v_2,...,v_n be vectors A_1A_2,A_2A_3,...,A_nA_1, respectively. P will be called regular, if there exist vectors u_1,...,u_n such that cross products  [u_1,u_2],[u_2,u_3],...,[u_n,u_1] are equal to vectors v_2,v_3,...,v_1, respectively. In this case the polygon P', defined be vectors u_2-u_1,u_3-u_2,...,u_1-u_n will be called the derived polygon or the derivative of the polygon P. In this work we formulate conditions for regularity and discuss geometric properties of derived polygons for n=4,5,6.