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 A215010 Integer side lengths in arithmetic progression of simple convex hexagons with equal interior angles. Sequence gives the values of m for sides of lengths t+m*d, counterclockwise, for the two primitive solutions. 0
 0, 5, 1, 3, 2, 4, 0, 5, 2, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Hexagons, such as (2,6,4,5,3,7), taken counterclockwise, can also be written (2,7,3,5,4,6) if considered clockwise or rotated 180 degrees and still read counterclockwise. Conjecture: hexagons are the only simple convex polygons with equal interior angles with such property, due to the fact that cos(Pi/3) = 1/2. The smaller such hexagon with all prime length sides is (7, 157, 67, 37, 127, 97). The smaller area of the two is sqrt(3)(6t^2 + 30td + 29d^2)/4 and the greater is sqrt(3)d^2/2 more. LINKS EXAMPLE If first term is t = 1 and common difference is d = 1, we get (1, 6, 2, 4, 3, 5) and (1, 6, 3, 2, 5, 4); two hexagons with equal interior angles and all sides with consecutive integer lengths. If t = 5 and d = 6 we get (5, 35, 11, 23, 17, 29) and (5, 35, 17, 11, 29, 23). CROSSREFS Sequence in context: A342375 A055515 A338096 * A136744 A068237 A083345 Adjacent sequences:  A215007 A215008 A215009 * A215011 A215012 A215013 KEYWORD nonn,fini AUTHOR Robin Garcia, Jul 31 2012 STATUS approved

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Last modified April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)