四面体的高度函数分解
Decompositions of Tetrahedra into Height Functions
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中文总结 AI 辅助
本文对四面体进行二面角分类，证明四面体要么是高度函数，要么经一次平面平分可得到两个高度函数四面体，且此类平分属于无穷多族平分。
中文摘要 AI 辅助
简言之，我们称多面体P为高度函数，当且仅当存在P的某个面F，使得P正交投影到包含F的仿射平面时完全落在F内。由于四面体存在多种构型，我们提出四面体的二面角分类，并证明四面体T要么本身就是高度函数，要么最多只需一次平面平分即可得到两个高度函数四面体。此外，我们还证明此类平分属于无穷多族平分。
英文摘要
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.
