For finite abstract simplicial complex $\Sigma$, initial realization $\alpha$ in $\mathbb{E}^d$, and desired edge lengths $L$, we give practical sufficient conditions for the existence of a non-self-intersecting perturbation of $\alpha$ realizing the lengths $L$. We provide software to verify these conditions by computer and optionally assist in the creation of an initial realization from abstract simplicial data. Applications include proving the existence of a planar embedding of a graph with specified edge lengths or proving the existence of polyhedra (or higher-dimensional polytopes) with specified edge lengths.

翻译：摘要：对于有限抽象单纯复形 $\Sigma$，其在 $\mathbb{E}^d$ 中的初始实现 $\alpha$ 以及目标边长 $L$，我们给出了非自交扰动 $\alpha$ 以实现边长 $L$ 存在的实用充分条件。我们提供了软件以通过计算机验证这些条件，并可选择协助从抽象单纯数据创建初始实现。其应用包括证明具有指定边长的图的平面嵌入的存在性，或证明具有指定边长的多面体（或更高维多胞体）的存在性。