Visualization of Polyhedra with Virtual Reality (VR) in A-frame
author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português
Archimedes and Catalan Dragon Fractals
The dragon curve belongs to the family of self-similar fractal curves, which can be approximated by recursive methods. The dragon curve is probably most commonly thought of as the shape that is generated from a strip of paper repeatedly folded in half.
This work shows Archimedean and Catalan polyhedra forming dragon fractals, modeled for visualization in Virtual Reality.
3D models
1. Icosidodecahedron
Applying the construction principle of the dragon curve with the icosidodecahedron, we obtain a icosidodecahedron dragon fractal. In the first order of construction of the fractal, we construct two new icosidodecahedron corresponding to one original polyhedron. In this example, we have solid representations in orders from 0 to 10.
2. Rhombicuboctahedron
Rhombicuboctahedron dragon fractal.
3. Cuboctahedron
Cuboctahedron dragon fractal.
4. Rhombicosidodecahedron
Rhombicosidodecahedron dragon fractal.
5. Truncated dodecahedron
Truncated dodecahedron dragon fractal.
6. Truncated tetrahedron
Truncated tetrahedron dragon fractal.
7. Truncated icosahedron
Truncated icosahedron dragon fractal.
8. Truncated icosidodecahedron
Truncated icosidodecahedron dragon fractal.
9. Snub dodecahedron
Snub dodecahedron dragon fractal.
10. Truncated octahedron
Truncated octahedron dragon fractal.
11. Truncated cube
Truncated cube dragon fractal.
12. Truncated cuboctahedron
Truncated cuboctahedron dragon fractal.
13. Snub cube
Snub cube dragon fractal.
14. Deltoidal hexecontahedron
Deltoidal hexecontahedron dragon fractal.
15. Deltoidal icositetrahedron
Deltoidal icositetrahedron dragon fractal.
16. Disdyakis dodecahedron
Disdyakis dodecahedron dragon fractal.
17. Triakis octahedron
Triakis octahedron dragon fractal.
18. Triakis tetrahedron
Triakis tetrahedron dragon fractal.
19. Triakis icosahedron
Triakis icosahedron dragon fractal.
20. Pentagonal icositetrahedron
Pentagonal icositetrahedron dragon fractal.
21. Disdyakis triacontahedron
Disdyakis triacontahedron dragon fractal.
22. Rhombic triacontahedron
Rhombic triacontahedron dragon fractal.
23. Pentakis dodecahedron
Pentakis dodecahedron dragon fractal.
24. Tetrakis hexahedron
Tetrakis hexahedron dragon fractal.
25. Pentagonal hexecontahedron
Pentagonal hexecontahedron dragon fractal.
26. Rhombic dodecahedron
Rhombic dodecahedron dragon fractal.
Archimedes and Catalan dragon fractals: polyhedra and visualization 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., "Archimedes and Catalan dragon fractals: polyhedra and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/polyhedra3/dragon-archimedes/>, March 2025.
References:
Weisstein, Eric W. “Archimedean Solid” From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/ArchimedeanSolid.html
McCooey, D. I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/