  This article introduces a theory of proximal nerve complexes and nerve
spokes, restricted to the triangulation of finite regions in the Euclidean
plane. A nerve complex is a collection of filled triangles with a common
vertex, covering a finite region of the plane. Structures called $k$-spokes,
$k\geq 1$, are a natural extension of nerve complexes. A $k$-spoke is the union
of a collection of filled triangles that pairwise either have a common edge or
a common vertex. A consideration of the closeness of nerve complexes leads to a
proximal view of simplicial complexes. A practical application of proximal
nerve complexes is given, briefly, in terms of object shape geometry in digital
images.
