Symmetric Independent Families of Four Isosceles Triangles
This Demonstration shows symmetric independent families of four isosceles triangles with up to 18 regions.
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].
 B. Grünbaum, "The Search for Symmetric Venn Diagrams," Geombinatorics, 8(4), 1999 pp. 104–109. (Apr 4, 2019) sites.math.washington.edu/~grunbaum/SymmetricVennDiagrams.pdf.