Basic geometric proof of the relation between dimensionality of a regular simplex and its dihedral angle

TL;DR

This paper provides a fundamental geometric proof linking the dimensionality of a regular simplex to its dihedral angle, specifically deriving the formula arccos(1/n) using classical geometric methods.

Contribution

It offers a basic geometric derivation of the dihedral angle formula for regular simplices across dimensions, clarifying the relationship between dimension and dihedral angle.

Findings

Derived the dihedral angle formula arccos(1/n) for n-dimensional regular simplices

Established a geometric connection between simplex dimension and dihedral angle

Provided a classical geometric proof for the relation

Abstract

The formula for the dihedral angle of the simplex of n dimensions, arccos(1/n), is derived using classical geometry.