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
Regular polygonal and composition toroids 3
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:
This work shows regular polygonal and composition toroids modeled in 3D, with views that can be accessed with resources in immersive Virtual Reality rooms.
3D models
1. Cube
A toroid constructed from a cube, with constructions based on the work of Rinus Roelofs: each polyhedron is constructed with triangular connections that form equal angles between its faces.
2. Cube v2
A toroid constructed from a cube, with constructions based on the work of Rinus Roelofs: each polyhedron is constructed with triangular connections that form equal angles between its faces.
3. Cuboctahedron
A toroid constructed from a cube, with constructions based on the work of Rinus Roelofs.
4. Deltoidal icositetrahedron
A toroid constructed from a deltoidal icositetrahedron, with constructions based on the work of Rinus Roelofs.
5. Dodecahedron
A toroid constructed from a dodecahedron, with constructions based on the work of Rinus Roelofs.
6. Dodecahedron v2
A toroid constructed from a dodecahedron, with constructions based on the work of Rinus Roelofs.
7. Dodecahedron v3
A toroid constructed from a dodecahedron, with constructions based on the work of Rinus Roelofs.
8. Dodecahedron v4
A toroid constructed from a dodecahedron, with constructions based on the work of Rinus Roelofs.
9. Hexakis tetrahedron
A toroid constructed from a hexakis tetrahedron, with constructions based on the work of Rinus Roelofs.
10. Icosahedron
A toroid constructed from a icosahedron, with constructions based on the work of Rinus Roelofs.
11. Icosahedron v2
A toroid constructed from a icosahedron, with constructions based on the work of Rinus Roelofs.
12. Octahedron
A toroid constructed from a octahedron, with constructions based on the work of Rinus Roelofs.
13. Octahedron v2
A toroid constructed from a octahedron, with constructions based on the work of Rinus Roelofs.
14. Rhombicuboctahedron
A toroid constructed from a rhombicuboctahedron, with constructions based on the work of Rinus Roelofs.
15. Snub cube
A toroid constructed from a snub cube, with constructions based on the work of Rinus Roelofs.
16. Square gyrobicupola
A toroid constructed from a square gyrobicupola, with constructions based on the work of Rinus Roelofs.
17. Square orthobicupola
A toroid constructed from a square orthobicupola, with constructions based on the work of Rinus Roelofs.
18. Tetrahedron
A toroid constructed from a tetrahedron, with constructions based on the work of Rinus Roelofs.
19. Tetrahedron v2
A toroid constructed from a tetrahedron, with constructions based on the work of Rinus Roelofs.
20. Tetrakis hexahedron
A toroid constructed from a tetrakis hexahedron, with constructions based on the work of Rinus Roelofs.
21. Triangular orthobicupola
A toroid constructed from a triangular orthobicupola, with constructions based on the work of Rinus Roelofs.
22. Truncated icosahedron
A toroid constructed from a truncated icosahedron, with constructions based on the work of Rinus Roelofs.
Regular polygonal and composition toroids 3: 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., "Regular polygonal and composition toroids 3: visualization of solids with Virtual Reality". Available in: <https://paulohscwb.github.io/torus-toroids/regular3/>, June 2026.
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/