Amicable Lattice Rhombuses are Amicable
Metric Geometry
2026-05-20 v1
Abstract
A polygon is equable if its area is equal to its perimeter. A pair of polygons is an amicable pair if the area of the first is equal to the perimeter of the second, and vice versa. A polygon is a lattice polygon if its vertices lie on the integer lattice. We show that amicable lattice rhombuses are actually equable.
Keywords
Cite
@article{arxiv.2605.20093,
title = {Amicable Lattice Rhombuses are Amicable},
author = {Bohdan Biekietov and Iwan Praton and Weiran Zeng},
journal= {arXiv preprint arXiv:2605.20093},
year = {2026}
}