On the number of non-congruent lattice tetrahedra

TL;DR

This paper investigates the quantity of distinct lattice tetrahedra within a truncated three-dimensional integer grid, demonstrating that their number grows significantly as the grid size increases.

Contribution

It establishes a lower bound on the number of non-congruent lattice tetrahedra in a finite cubic lattice, highlighting their abundance.

Findings

Number of non-congruent lattice tetrahedra increases with grid size

Provides bounds on the count of such tetrahedra

Shows richness of lattice tetrahedral configurations

Abstract

We prove that there are "many" non-congruent tetrahedra in the truncated lattice $[0,q]^3\cap \mathbb{Z}^3$.