Tiling space and slabs with acute tetrahedra

TL;DR

This paper demonstrates that three-dimensional space can be tiled exclusively with tetrahedra having acute dihedral angles, providing multiple constructions including a universal tiling and a slab tiling.

Contribution

It introduces new methods for tiling space with only acute tetrahedra, expanding understanding of geometric tilings and their angle constraints.

Findings

Space can be tiled with tetrahedra all having dihedral angles less than 77.08°

A construction for tiling a slab with acute tetrahedra is provided

Multiple constructions demonstrate the feasibility of acute tetrahedral tilings

Abstract

We show it is possible to tile three-dimensional space using only tetrahedra with acute dihedral angles. We present several constructions to achieve this, including one in which all dihedral angles are less than $77.08^\circ$, and another which tiles a slab in space.