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A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Your job is to find out if a given polygon is regular or not.

Specs

  • You will be given a list of Cartesian coordinate 2-tuples which describe the polygon's vertices.
  • The points will always make a valid polygon.
  • You have to return a truthy / falsey for whether or not the polygon is regular.
  • Assume vertices are rounded to the nearest int.
  • They might or might not be in order.
  • This is so shortest code in bytes wins!

Test Cases

Most test cases generated by this site.

[(1,2), (3, 2), (1, 0), (3, 0)] -> True
[(1, 1), (5, 3), (7, 7), (3, 5)] -> False
[(550,450), (455,519), (491,631), (609,631), (645,519)] -> True
[(106,81), (94,81), (84,88), (80,100), (84,112), (94,119), (106,119), (116,112), (120,100), (116,88)] -> True
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  • \$\begingroup\$ Are the coordinates always integers? \$\endgroup\$ – Reto Koradi Dec 7 '15 at 3:59
  • \$\begingroup\$ Another question: Based on the examples, it looks like the vertices are not necessarily in order? \$\endgroup\$ – Reto Koradi Dec 7 '15 at 4:09
  • \$\begingroup\$ Surely a polygon with all integer coordinates cannot be regular unless it's a square? Are we assuming some rounding? \$\endgroup\$ – xnor Dec 7 '15 at 4:28
  • \$\begingroup\$ @xnor sorry forgot to mention, you're rounding to nearest int. \$\endgroup\$ – Maltysen Dec 7 '15 at 4:32
  • \$\begingroup\$ @RetoKoradi correct. they are in any order, updated question. \$\endgroup\$ – Maltysen Dec 7 '15 at 4:33

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