Tile Count in the Interior of Regular 2n-gons Dissected by Diagonals Parallel to Sides

TL;DR

This paper investigates the number of tiles formed inside regular 2n-gons when dissected by diagonals parallel to sides, providing detailed counts up to the 78-gon.

Contribution

It offers a comprehensive enumeration of tiles in regular 2n-gons dissected by specific diagonals, extending previous work to polygons with up to 78 sides.

Findings

Number of tiles for regular 2n-gons up to n=39.

Pattern identification in tile counts.

Potential formulas for tile enumeration.

Abstract

The regular 2n-gon (square, hexagon, octagon, ...) is subdivided into smaller polygons (tiles) by the subset of diagonals which run parallel to any of the 2n sides. The manuscript reports on the number of tiles up to the 78-gon.