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An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space.Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points.
The second circle is centered at any point on the first circle. All following circles are centered on the intersection of two other circles. The design is sometimes expanded into a regular overlapping circles grid. Bartfeld (2005) describes the construction: "This design consists of circles having a 1-[inch] radius, with each point of ...
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The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
However personally I don't think that Goldberg polyhedra are valid representations of Overlapping circles grid at all, because the circles required for one lattice type will be different from those of the other (From memory, a triangular grid sections the circle in 60 degree slices, while a pentagonal leads to 72 degree slices). This implies ...
The original can be viewed here: Circle with overlapping manifold charts.png: . Modifications made by Pbroks13 . This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.