# Separation in Simply Linked Neighbourly 4-Polytopes

## TL;DR

This paper investigates the separation problem in convex geometry, verifying a conjecture about the maximum number of hyperplanes needed to separate a point from all faces in a specific class of 4-polytopes.

## Contribution

It proves the conjecture for simply linked neighbourly 4-polytopes, advancing understanding of hyperplane separation in convex polytopes.

## Key findings

- Verified the conjecture s(O,K) ≤ 2^d for simply linked neighbourly 4-polytopes
- Established bounds on hyperplane separation in specific convex polytopes
- Contributed to the theory of convex polytope separation problems

## Abstract

The Separation Problem asks for the minimum number s(O,K) of hyperplanes required to strictly separate any interior point O of a convex body K from all faces of K. The Conjecture is s(O,K) is at most 2 to the power d in real d-space , and we verify this for the class of simply linked neighbourly 4-polytopes.