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.

(box: x-ray)  (slider: perspective)  (image: L=rotate R=zoom)
Please use a browser that supports "canvas"

Klein Map {7,3}8 (basic shape)
Please use a browser that supports "canvas"

Klein Map Dual {3,7}8 (Schulte & Wills)
Please use a browser that supports "canvas"

Regular Map {6,4}10 (Schulte & Wills)
Please use a browser that supports "canvas"

Regular Map {4,6}10 (Schulte & Wills)
Please use a browser that supports "canvas"

Heptagonal Dodecahedron (type A) (C3-symmetric form 3)
Please use a browser that supports "canvas"

Heptagonal Dodecahedron (type A) (S4-symmetric form 1)
Please use a browser that supports "canvas"

Heptagonal Dodecahedron (type B) (form 1)
Please use a browser that supports "canvas"

Heptagonal Dodecahedron (type C) (form 1)
Please use a browser that supports "canvas"

Heptagonal Dodecahedron (type D) (form 3)
Please use a browser that supports "canvas"

Heptagonal Dodecahedron (type E) (form 1)