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.

• Incircle
• Inclusion-Exclusion Principle
• Inclusion Map
• Incommensurate
• Incomplete Gamma Function
• Incompleteness
• Increasing Function
• Increasing Sequence
• Indefinite Integral
• Indefinite Quadratic Form
• Indegree
• Independence Axiom
• Independence Complement Theorem
• Independence Number
• Independent Equations
• Independent Sequence
• Independent Statistics
• Independent Vertices
• Indeterminate Problems
• Index
• Index Set
• Index Theory
• Indicatrix
• Indicial Equation
• Indifference Principle