THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. June 2005), DS #5.

Venn Diagram Survey
Some Symmetric k-fold 2-Venn Diagrams


Mirror-image symmetry

On the left: Grünbaum's coiled snakes. A k-fold 2-Venn diagram with mirror image symmetry. Shown with k = 4. Other values of k may be obtained by twisting/untwisting the tails.

Rotational symmetry

Grünbaum's rotated F's. A (2k+1)-fold 2-Venn diagram with rotational symmetry. Shown with k = 1. Additional twists of both ends give larger values of k. Another Grünbaum example. A 2k-fold 2-Venn diagram with rotational symmetry. Shown with k = 3. Additional twists/untwists of both ends give other values of k. Note that the curves passing through the red vertices do not meet transversally.


THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. June 2005), DS #5.