Geometry

Transformation of an Equilateral Irregular Dodecagon to a Regular Icositetragon Via Radiocentric Mapping on a Duodecimal Lattice

Authors: Eric A. Larsen
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This paper demonstrates a geometric transformation that maps an irregular, equilateral 12-sided polygon (dodecagon) to a perfectly regular 24-sided polygon (icositetragon). By constructing the initial Cartesian plane over a duodecimal (base-12) lattice, we eliminate decimal truncation errors and establish exact coordinates for side lengths uniformly measuring (frac{5}{12}sqrt{2}) (expressed as (0.5sqrt{2}_{12})). We show that scaling this system by a dilation factor of 4, followed by a radiocentric rearrangement of the segments along a splayed 48-radial symmetry matrix—derived from the classical Flower of Life construct—forces the perimeter segments into an equiangular configuration. A formal geometric proof is presented to confirm that the resulting transformed figure is perfectly equilateral and equiangular, thereby achieving complete regularity.
Category: Geometry