Cyclic Averages of Regular Polygons and Platonic Solids


  • Mamuka Meskhishvili Department of Mathematics, Georgian-American High School, 18 Chkondideli Str., Tbilisi 0180



Regular polygon, Platonic solid, Circle, Sphere, Locus, Sum of like powers, Rational distances problem


The concept of the cyclic averages are introduced for a regular polygon \(P_n\) and a Platonic solid \(T_n\). It is shown that cyclic averages of equal powers are the same for various \(P_n(T_n)\), but their number is characteristic of \(P_n(T_n)\). Given the definition of a circle (sphere) by the vertices of \(P_n(T_n)\) and on the base of the cyclic averages are established the common metrical relations of \(P_n(T_n)\).


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How to Cite

Meskhishvili, M. (2020). Cyclic Averages of Regular Polygons and Platonic Solids. Communications in Mathematics and Applications, 11(3), 335–355.



Research Article