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arXiv · 2608.11217

Decompositions of Tetrahedra into Height Functions

Connor Castillo·Jackson Smith
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Abstract

In short, we call a polyhedron P a height function if there exists some face F of P such that P lies entirely within F when orthogonally projected onto the affine plane containing F. Because tetrahedra come in various configurations, we propose a dihedral angle classification of tetrahedra, and prove that a tetrahedron T is either a height function already, or, at most one planar bisection of T is needed to produce two height function tetrahedra. Furthermore, we prove that such bisections belong to infinitely large families of bisections.

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BibTeXRIS

Connor Castillo, Jackson Smith. 2026-07-21. Decompositions of Tetrahedra into Height Functions. https://arxiv.org/abs/2608.11217

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