# Projections of k-simplex onto the subsimplices of arbitrary type are derivations

## TL;DR

This paper proves that projections of arbitrary k-simplices onto certain subsimplices are derivations, expanding understanding of geometric projections in simplicial complexes.

## Contribution

It introduces a novel proof that such projections are derivations, providing new insights into the structure of simplices and their subsimplices.

## Key findings

- Projections of k-simplices onto subsimplices are derivations.
- The proof applies to arbitrary types of subsimplices.
- Enhances theoretical understanding of simplicial projections.

## Abstract

The aim of this paper is to prove that there is a projection of an arbitrary k-simplex onto (m - l)-subsimplex, where 1 < l < m < k - 1, which is a derivation.