# The Magic Permutohedron

## TL;DR

The paper introduces a special configuration called a magic permutohedron, where numbers are placed on vertices to satisfy specific sum conditions on squares and hexagons, revealing a novel combinatorial structure.

## Contribution

It presents the first known construction of a magic permutohedron with specific sum properties on its sides, expanding the understanding of combinatorial configurations.

## Key findings

- Numbers 1 to 24 are arranged to satisfy side sum conditions
- The configuration demonstrates a new type of combinatorial magic structure
- Potential applications in combinatorics and recreational mathematics

## Abstract

We present a configuration called a magic permutohedron that shows the placement of the numbers of $\{1, 2, 3, \dots, 24\}$ in the vertices of the permutohedra so that the sum of numbers on each square side is 50 and the sum of the numbers in each hexagonal side is 75.