Unified constructions of the regular Heptagon, Triskaidecagon and Heptadecagon

TL;DR

This paper presents new geometric constructions for regular heptagon, triskaidecagon, and heptadecagon using angle trisection, expanding on known methods and revealing symmetries related to Galois groups.

Contribution

It introduces novel constructions for these polygons based on angle trisection, extending previous work and highlighting algebraic symmetries.

Findings

Multiple new constructions for regular polygons using angle trisection.

Identification of symmetries related to Galois groups in these constructions.

Enhanced understanding of geometric and algebraic properties of these polygons.

Abstract

Constructions of regular heptagon and triskaidecagon by trisection of an angle are well known. An elegant construction of the heptagon by S. Adlaj shows a 3-fold symmetry related to a Galois group. Based on the latter construction, in this article one more for the heptagon, two more for the triskaidecagon and three for heptadecagon are presented, all using angle trisection.