Higher Genus Toroidal Solids

Higher Genus Toroidal Solids

A toroidal solid, or toroid, is an orientable polyhedron without self-intersections that has genus greater than zero, meaning that it contains one or more holes. An orientable polyhedron's genus (G) is related to the number of vertices (V), faces (F), and edges (E) as follows:

V + F − E = 2 − 2 * G

The toroids on this page all have genus 2 or higher.

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Klein Map {7,3}₈ (basic shape)	Klein Map Dual {3,7}₈ (Schulte & Wills)	Regular Map {6,4}₁₀ (Schulte & Wills)
Regular Map {4,6}₁₀ (Schulte & Wills)	Heptagonal Dodecahedron (type A) (C3-symmetric form 3)	Heptagonal Dodecahedron (type A) (S4-symmetric form 1)
Heptagonal Dodecahedron (type B) (form 1)	Heptagonal Dodecahedron (type C) (form 1)	Heptagonal Dodecahedron (type D) (form 3)
Heptagonal Dodecahedron (type E) (form 1)	Locally Regular Map {7,3} of Genus 5 (type A) (version 3)	Locally Regular Map {7,3} of Genus 11 (type A) (version 6)
Octagonal Dodecahedron with 8 overarching faces	Hendecagonal Dodecahedron with 12 overarching faces