The Background Pattern

The pattern behind some of my pages is of a tessellaton of the Poincare disk model of hyperbolic (or non-Euclidean) geometry.
The tessellation was discovered by Klein and is associated with G, the (2,3,7) triangle group, on which I have worked .
Any pair of adjacent triangles in the figure give a fundamental domain for G.
Many subgroups of G are clearly visible - for example the central heptagon corresponds to a subgroup of index 7.


More tessellations can be found at this location.
Similar ideas lie behind many of the works of Escher.


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