# On inscribed equilateral simplices in normed spaces

## TL;DR

This paper investigates the existence of large equilateral simplices inscribed in the unit ball of certain n-dimensional normed spaces, extending previous constructions and providing counterexamples.

## Contribution

It generalizes Makeev's 4-dimensional construction to higher dimensions and identifies spaces where the construction fails.

## Key findings

- Existence of large inscribed equilateral simplices in certain normed spaces
- Extension of Makeev's construction to higher dimensions
- Identification of spaces where the construction does not apply

## Abstract

In this paper we prove in certain n-dimensional normed spaces X the existence of full-dimensional equilateral simplices of large size inscribed to the unit ball B. This extends the construction of Makeev [Mak] in dimension 4 and we also compute an example of a space in which the idea cannot be applied.