Fundamental Definition and 947 Threads

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.
There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells.

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  1. T

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  2. B

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  3. P

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  4. A

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  5. H

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  6. M

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  7. bcrowell

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  8. C

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  9. N

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  10. C

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  11. O

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  12. H

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  13. L

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  14. K

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  15. Z

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  16. N

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  17. E

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  18. C

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  19. N

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  20. K

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  21. J

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  22. R

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  23. C

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  24. T

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  25. Z

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  26. P

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  27. J

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  32. O

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  33. D

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  34. S

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  35. R

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  36. S

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  37. T

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  38. L

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  39. S

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  40. L

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  41. Pythagorean

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  42. G

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  43. M

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  44. M

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  45. MTd2

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  46. Z

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  47. D

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  48. D

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  49. J

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  50. A

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