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spring-of-mathematics:

Unfolding of Spherical Surfaces. Make a paper model with an approximate pattern.
This patterns are really wonderful. Because, determining how to unfold a polyhedron or a sphere into a net is tricky.
For example, determining how to unfold a polyhedron: cuts cannot be made along all edges that surround a face or the face will completely separate. Furthermore, for a polyhedron with no coplanar faces, at least one edge cut must be made from each vertex or else the polyhedron will not flatten. In fact, the edges that must be cut corresponds to a special kind of graph called a spanning tree of the skeleton of the polyhedron (Malkevitch). Source.

See more: Unfolding at Mathworld.wolfram.com &  Dymaxion Map on Wikipedia.

Image: Catalouge by David Swart (Full Size) & Unfolding a 3D sphere to 2D shapes.

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