Cyclic Averages of Regular Polygons and Platonic Solids

Mamuka Meskhishvili

doi:10.26713/cma.v11i3.1420

paper

Cyclic Averages of Regular Polygons and Platonic Solids

arXiv:2010.12340 · doi:10.26713/cma.v11i3.1420

Abstract

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 $P_{n} (T_{n})$ .