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This paper introduces two proximal forms of Lenzen physical geometry, namely,an \emph{axiomatized strongly proximal physical geometry} that is built onsimplicial complexes with the dualities and sewing operations derived fromstring geometry and an \emph{axiomatized descriptive proximal physicalgeometry} in which spatial regions are described based on their features andthe descriptive proximities between regions. This is a computational proximityapproach to a Lenzen geometry of physical space. In both forms of physicalgeometry, region is a primitive. Intuitively, a region is a set of connectedsubregions. The primitive in this geometry is \emph{region}, instead of\emph{point}. Each description of a region with $n$ features is a mapping fromthe region to a feature vector in $\mathbb{R}^n$. In the feature space,proximal physical geometry has the look and feel of either Euclidean,Riemannian, or non-Euclidean geometry, since we freely work with the relationsbetween points in the feature space. The focus in these new forms of geometryis the relation between individual regions with their own distinctive featuressuch as shape, area, perimeter and diameter and the relation between nonemptysets of regions. The axioms for physical geometry as well as the axioms forproximal physical geometry are given and illustrated. Results for parallelclasses of regions, descriptive fibre bundles and BreMiller-Sloyer sheaves aregiven. In addition, a region-based Borsuk-Ulam Theorem as well as a WiredFriend Theorem are given in the context of both forms of physical geometry.

Two Forms of Proximal Physical Geometry. Axioms, Sewing Regions Together, Classes of Regions, Duality, and Parallel Fibre Bundles