Spherical Venn Diagrams with Involutory Isometries
Frank Ruskey,
Department of Computer Science,
University of Victoria, Canada.
Mark Weston,
Department of Computer Science,
University of Victoria, Canada.
Abstract:
Let f be an isometry of the sphere which is an involution
(that is, f^{1} = f).
For any $n \ge 1$ we prove that there is an $n$curve Venn diagram on the
sphere whose isometry group is generated by f and which has the
property that f(C) = C, where C is a curve of the diagram.
One of the constructions uses a new chain decomposition of the Boolean lattice,
a decomposition which is based on the wellknown decomposition of
N. G. de Bruijn, C. A. van Ebbenhorst Tengbergen, and D. R. Kruyswijk.
Polar symmetric 4Venn diagrams
The cyan vertices are identified.
On the left, reflect about the center of the sphere.
On the right, reflect about the axis through the cyan vertex.
These examples can be extended to any n.

The postscript file.

The pdf file.

Electronic Journal of Combinatorics, 18 (2011) #P191, 14 pages.

Original submission: September 2009.
Revised submission:
Acceptance: August 2011.