Blending Polyhedra with Overlays

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Douglas Zongker and George W. Hart: Blending Polyhedra with Overlays. In: Bridges 2001. Pages 167–174



We introduce a novel method for constructing polyhedra by blending together two or more existing polyhedra, using a dualizationmethod. The method results in a Minkowski sum, analogous to that of overlay tHings [5], which uses a topological dual operation to create tilings from a network (a graph . embedded in a plane). This paper extends that method to networks on the surface of the unit sphere. We begin with polyhedra in canonical form, dualize them to form networks, overlay the networks, and dualize the result to obtain a new polyhedron that blends together the faces of the original polyhedra.

Extended Abstract


Used References

[1] George W. Hart. Calculating canonical polyhedra. Mathematica in Education and Research, 6(3):5-10, Summer 1997.

[2] George W. Hart. Zonish polyhedra. In Proceedings of Mathematics and Design '98, page 653, 1998.

[3] George W. Hart and Henri Picciotto. Zome Geometry. Key Curriculum Press, 2001.

[4] Gunter M. Ziegler. Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics. Springer-Verlag, 1994.

[5] Douglas Zongker. Creation of overlay tilings through dualization of regular networks. In Nathaniel Friedman and Javier Barrallo, editors, Proceedings of ISAMA 99, pages 495-502, June 1999.


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