Torus and Toroids: visualization of solids with Augmented Reality (AR) and Virtual Reality (VR) in A-frame

author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português

More solids: Torus and toroids Tetragonal toroids Iris toroids Regular tetragonal toroids Möbius, Vélez-Jahn and Cairo toroids Hexagonal toroids Regular polygonal and composition toroids 1

Iris toroids

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

This work shows iris toroids modeled in 3D, with views that can be accessed with resources in immersive Virtual Reality rooms.

3D Models  |  Home

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3D models

1. Anti Hexagonal Iris Toroid

faces: 12 isosceles triangles and 12 scalene triangles | vertices: 12 | edges: 36

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2. Anti Heptagonal Iris Toroid

faces: 14 isosceles triangles and 14 scalene triangles | vertices: 14 | edges: 42

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3. Anti Octagonal Iris Toroid

faces: 16 isosceles triangles and 16 scalene triangles | vertices: 16 | edges: 48

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4. Anti Enneagonal Iris Toroid {9/3}

faces: 18 isosceles triangles and 18 scalene triangles | vertices: 18 | edges: 54

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5. Anti Enneagonal Iris Toroid {9/4}

faces: 18 isosceles triangles and 18 scalene triangles | vertices: 18 | edges: 54

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6. Anti Decagonal Iris Toroid {10/3}

faces: 20 isosceles triangles and 20 scalene triangles | vertices: 20 | edges: 60

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7. Anti Decagonal Iris Toroid {10/4}

faces: 20 isosceles triangles and 20 scalene triangles | vertices: 20 | edges: 60

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8. Pentagonal Iris Toroid

faces: 5 rectangles and 10 scalene triangles | vertices: 10 | edges: 25

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9. Hexagonal Iris Toroid

faces: 6 rectangles and 12 scalene triangles | vertices: 12 | edges: 30

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10. Heptagonal Iris Toroid {7/3}

faces: 7 rectangles and 14 scalene triangles | vertices: 14 | edges: 35

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11. Heptagonal Iris Toroid {7/2}

faces: 7 rectangles and 14 scalene triangles | vertices: 14 | edges: 35

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12. Octagonal Iris Toroid {8/3}

faces: 8 rectangles and 16 scalene triangles | vertices: 16 | edges: 40

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13. Octagonal Iris Toroid {8/2}

faces: 8 rectangles and 16 scalene triangles | vertices: 16 | edges: 40

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14. Enneagonal Iris Toroid {9/4}

faces: 9 rectangles and 18 scalene triangles | vertices: 18 | edges: 45

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15. Enneagonal Iris Toroid {9/3}

faces: 9 rectangles and 18 scalene triangles | vertices: 18 | edges: 45

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16. Enneagonal Iris Toroid {9/2}

faces: 9 rectangles and 18 scalene triangles | vertices: 18 | edges: 45

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17. Decagonal Iris Toroid {10/4}

faces: 10 rectangles and 20 scalene triangles | vertices: 20 | edges: 50

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18. Decagonal Iris Toroid {10/3}

faces: 10 rectangles and 20 scalene triangles | vertices: 20 | edges: 50

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19. Decagonal Iris Toroid {10/2}

faces: 10 rectangles and 20 scalene triangles | vertices: 20 | edges: 50

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Iris toroids: visualization of solids with Virtual Reality by Paulo Henrique Siqueira is licensed with a license Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International.

How to cite this work:

Siqueira, P.H., "Iris toroids: visualization of solids with Virtual Reality". Available in: <https://paulohscwb.github.io/torus-toroids/iris/>, April 2025.

References:
Weisstein, Eric W. “Torus” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/Torus.html
Weisstein, Eric W. “Toroid” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/Toroid.html
McCooey, D. I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/