Non-Regular 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

A toroid is said to be non-regular if not all of its faces have the same number of vertices, or not all of its vertices join the same number of faces. All of the toroids on this page are non-regular.

(box: x-ray)  (slider: perspective)  (image: L=rotate R=zoom)
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Isohedral Toroid with 24 faces
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Toroid with regular faces
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Knotted Dodecahedron
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Cairo-Tiling Toroid with 8 overarching faces (version 1)
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Cairo-Tiling Toroid with 16 faces (type A) (8 faces overarching)
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Cairo-Tiling Toroid with 16 faces (type B) (square form)
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Cairo-Tiling Toroid with 16 faces (type C) (boomerang form)
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Cube-Octahedron Toroid
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Tetragonal Trapezohedron-Antiprism Toroid
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Pentagonal Trapezohedron-Antiprism Toroid
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Hexagonal Trapezohedron-Antiprism Toroid
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Square Antiprism-Trapezohedron Toroid
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Pentagonal Antiprism-Trapezohedron Toroid
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Hexagonal Antiprism-Trapezohedron Toroid
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Tetragonal Trapezohedron Toroid
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Pentagonal Trapezohedron Toroid
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Hexagonal Trapezohedron Toroid
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Heptagonal Iris Toroid
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Octagonal Iris Toroid