Toroidal Polyhedron

A toroidal polyhedron is a Polyhedron with Genus (i.e., having one or moreHoles). Examples of toroidal polyhedra include the Császár Polyhedron andSzilassi Polyhedron, both of which have Genus 1 (i.e., the Topology of aTorus).

The only known Toroidal Polyhedron with no Diagonals is the CsászárPolyhedron. If another exists, it must have 12 or more Vertices and Genus . The smallest known single-hole toroidal Polyhedronmade up of only Equilateral Triangles is composed of 48 of them.

References

Gardner, M. Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, p. 141, 1988.

Hart, G. ``Toroidal Polyhedra.'' http://www.li.net/~george/virtual-polyhedra/toroidal.html.

Stewart, B. M. Adventures Among the Toroids, 2nd rev. ed. Okemos, MI: B. M. Stewart, 1984.

• Maltese Cross
• Maltese Cross Curve
• Malthusian Parameter
• Mandelbar Set
• Mandelbrot Set
• Mandelbrot Tree
• Mangoldt Function
• Manifold
• Mantissa
• Map
• Map Coloring
• Mapes' Method
• Map Folding
• Mapping (Function)
• Mapping Space
• Map Projection
• Marginal Analysis
• Marginal Probability
• Markoff Number
• Markoff's Formulas
• Markov Algorithm
• Markov Chain
• Markov Matrix
• Markov Moves
• Markov Number