# The minimum angle condition for $d$-simplices

## TL;DR

This paper generalizes the minimum angle condition from 2D triangulations to simplicial meshes in higher dimensions, establishing its equivalence with other mesh regularity conditions.

## Contribution

It introduces a natural extension of the minimum angle condition to higher-dimensional simplicial meshes and proves its equivalence with other mesh regularity criteria.

## Key findings

- The generalized minimum angle condition is equivalent to other mesh regularity conditions.
- The extension applies to simplicial meshes in any space dimension.
- Provides theoretical foundation for mesh quality in finite element analysis.

## Abstract

In this note we present a natural generalization of the minimum angle condition, commonly used in the finite element analysis for planar triangulations, to the case of simplicial meshes in any space dimension. The equivalence of this condition with some other mesh regularity conditions is proved.