# Translation of "Simplizialzerlegungen von Beschrankter Flachheit'' by Hans Freudenthal, Annals of Mathematics, Second Series, Volume 43, Number 3, July 1942, Pages 580-583

## TL;DR

This paper translates Freudenthal's 1942 work addressing Brouwer's question by constructing an infinite subdivision sequence of polytopes that avoids arbitrarily flat subsimplices, contributing to geometric topology.

## Contribution

It provides an English translation of Freudenthal's original paper, clarifying his method for subdividing polytopes without flattening subsimplices.

## Key findings

- Constructed an infinite subdivision sequence of polytopes
- Ensured subsimplices do not become arbitrarily flat
- Addressed Brouwer's question on polytope subdivision

## Abstract

Translation of the paper ``Simplizialzerlegungen von Beschrankter Flachheit'' by Hans Freudenthal (https://doi.org/10.2307/1968813), in which Freudenthal answers ``a question by Brouwer about the construction of an infinite series of subdivisions of a polytope, such that the next element in the sequence is a subdivision of the previous one and such that the subsimplices that arise do not become arbitrarily flat.''