Symmetric Independent Families of Four Isosceles Triangles

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This Demonstration shows symmetric independent families of four isosceles triangles with up to 18 regions.

Contributed by: Izidor Hafner (April 2019)
Open content licensed under CC BY-NC-SA



Consider a family of simple (Jordan) curves that intersect pairwise in finitely many points. Let be either the interior or the exterior of . The family is called independent if

for each of the possible choices of the . If, moreover, each of the sets is connected, the independent family is called a Venn diagram. An independent family or Venn diagram is called simple if no three curves have a common point [1, p. 104].

An example with equilateral triangles is from [1, p. 107].


[1] B. Grünbaum, "The Search for Symmetric Venn Diagrams," Geombinatorics, 8(4), 1999 pp. 104–109. (Apr 4, 2019)

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