THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. March 2001), DS #5.

# Venn Diagram Survey Diagrams Made from Triangles

There is a simple symmetric 5-Venn diagram in which each curve is a triangle; see Grunbaum and Winkler [GW]. Grünbaum [Gr84b] asked whether there was a 6-Venn diagram made from triangles. This question was recently answered in the affirmative by Jeremy Carroll [Ca99]. Below is his first example. He has subsequently discovered that there are exactly 126 different 6-Venn diagrams that can be drawn with each curve a triangle.

Below is a table of coordinates for the six triangles.

(x1,y1) (x2,y2) (x3, y3)
(-69277, -32868) (135580, 121186) (70900, 199427)
(333561, 225349) (61764, 76805) (38980, 182461)
(81988, -44426) (38444, 206222) (121044, 165111)
(-60184, 274046) (142476, 39903) (103276, 183962)
(131886, 385785) (38136, 111491) (94208, 24690)
(203271, 9619) (39604, 82683) (84652, 206669)

Below is another nicer example (this jpeg image courtesy of Jeremy Carroll). See his web page [JC] for further examples like this.

 THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. March 2001), DS #5.