Visualization of Fractal curves with polyhedra in Virtual Reality (VR) with A-frame
author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português
E.T. curve fractals with polyhedra
The E.T. fractal curve is formed by 4 segments of equal size, generated in each iteration. Using a 120° slope of the first segment relative to the x-axis, we have the formation of this fractal that resembles the character from the movie E.T., the extraterrestrial.
This work shows E.T. fractal curve with polyhedra, modeled for visualization in Virtual Reality.
3D models
1. Tetrahedron
Applying the construction principle of the E.T. curve fractal with the tetrahedron, we obtain an tetrahedron E.T. curve fractal. In the first order of construction of the fractal, we construct four new tetrahedra corresponding to one original polyhedron. In this example, we have solid representations in orders from 0 to 6.
2. Cube
E.T. curve fractal of cube.
3. Dodecahedron
E.T. curve fractal of dodecahedron.
4. Icosahedron
E.T. curve fractal of icosahedron.
5. Octahedron
E.T. curve fractal of octahedron.
6. Great dodecahedron
E.T. curve fractal of great dodecahedron.
7. Tetrakis hexahedron
E.T. curve fractal of tetrakis hexahedron.
8. Great icosahedron
E.T. curve fractal of great icosahedron.
9. Great triakis icosahedron
E.T. curve fractal of great triakis icosahedron.
10. Escher solid
E.T. curve fractal of Escher solid.
11. Small stellated dodecahedron
E.T. curve fractal of small stellated dodecahedron.
12. Great stellated dodecahedron
E.T. curve fractal of great stellated dodecahedron.
13. Cuboctahedron
E.T. curve fractal of cuboctahedron.
14. Snub cube
E.T. curve fractal of snub cube.
15. Truncated icosahedron
E.T. curve fractal of truncated icosahedron.
16. Snub dodecahedron
E.T. curve fractal of snub dodecahedron.
17. Tetrahemihexahedron
E.T. curve fractal of tetrahemihexahedron.
18. Tetrahemihexacron
E.T. curve fractal of tetrahemihexacron.
19. Hexahemioctacron
E.T. curve fractal of hexahemioctacron.
20. Small icosihemidodecacron
E.T. curve fractal of small icosihemidodecacron.
21. Small dodecahemicosahedron
E.T. curve fractal of small dodecahemicosahedron.
22. Great dodecahemicosahedron
E.T. curve fractal of great dodecahemicosahedron.
23. Stella octangula
E.T. curve fractal of stella octangula.
24. Concave dodecahedron
E.T. curve fractal of concave dodecahedron.
25. Jessens orthogonal icosahedron
E.T. curve fractal of Jessens orthogonal icosahedron.
26. Dyakis dodecahedron
E.T. curve fractal of dyakis dodecahedron.
27. Small hexacronic icositetrahedron
E.T. curve fractal of small hexacronic icositetrahedron.
28. Great hexacronic icositetrahedron
E.T. curve fractal of great hexacronic icositetrahedron.
29. Small icosicosidodecahedron
E.T. curve fractal of small icosicosidodecahedronn.
30. Dodecadodecahedron
E.T. curve fractal of dodecadodecahedron.
31. Medial rhombic triacontahedron
E.T. curve fractal of medial rhombic triacontahedron.
32. Medial triambic icosahedron
E.T. curve fractal of medial triambic icosahedron.
33. Small ditrigonal dodecacronic hexecontahedron
E.T. curve fractal of small ditrigonal dodecacronic hexecontahedron.
34. Great triambic icosahedron
E.T. curve fractal of great triambic icosahedron.
35. Great cubicuboctahedron
E.T. curve fractal of great cubicuboctahedron.
36. Uniform great rhombicuboctahedron
E.T. curve fractal of uniform great rhombicuboctahedron.
37. Great rhombihexahedron
E.T. curve fractal of great rhombihexahedron.
38. Small rhombihexacron
E.T. curve fractal of small rhombihexacron.
39. Great rhombihexacron
E.T. curve fractal of great rhombihexacron.
40. Small dodecicosacron
E.T. curve fractal of small dodecicosacron.
41. Small dodecicosahedron
E.T. curve fractal of small dodecicosahedron.
42. Rhombicosahedron
E.T. curve fractal of rhombicosahedron.
43. Rhombicosacron
E.T. curve fractal of rhombicosacron.
44. Cubitruncated cuboctahedron
E.T. curve fractal of cubitruncated cuboctahedron.
45. Tetradyakis hexahedron
E.T. curve fractal of tetradyakis hexahedron.
46. Great triakis octahedron
E.T. curve fractal of great triakis octahedron.
47. Great truncated cuboctahedron
E.T. curve fractal of great truncated cuboctahedron.
48. Great disdyakis dodecahedron
E.T. curve fractal of great disdyakis dodecahedron.
49. Truncated great dodecahedron
E.T. curve fractal of truncated great dodecahedron.
50. Small stellapentakis dodecahedron
E.T. curve fractal of small stellapentakis dodecahedron.
51. Tridyakis icosahedron
E.T. curve fractal of tridyakis icosahedron.
52. Truncated great icosahedron
E.T. curve fractal of truncated great icosahedron.
53. Great stellapentakis dodecahedron
E.T. curve fractal of great stellapentakis dodecahedron.
54. Medial disdyakis triacontahedron
E.T. curve fractal of medial disdyakis triacontahedron.
55. Great triakis icosahedron
E.T. curve fractal of great triakis icosahedron.
56. Great disdyakis triacontahedron
E.T. curve fractal of great disdyakis triacontahedron.
57. Joined truncated cube
E.T. curve fractal of joined truncated cube.
58. Chamfered octahedron
E.T. curve fractal of chamfered octahedron.
59. Rhombic dodecahedron
E.T. curve fractal of rhombic dodecahedron.
60. Triakis octahedron
E.T. curve fractal of triakis octahedron.
61. Deltoidal icositetrahedron
E.T. curve fractal of deltoidal icositetrahedron.
62. Pentagonal icositetrahedron
E.T. curve fractal of pentagonal icositetrahedron.
63. Disdyakis dodecahedron
E.T. curve fractal of disdyakis dodecahedron.
64. Icosidodecahedron
E.T. curve fractal of icosidodecahedron.
65. Rhombicuboctahedron
E.T. curve fractal of rhombicuboctahedron.
66. Truncated tetrahedron
E.T. curve fractal of truncated tetrahedron.
67. Hendecagonal dodecahedron
E.T. curve fractal of hendecagonal dodecahedron.
68. Klein map
E.T. curve fractal of Klein map.
69. Joined truncated tetrahedron
E.T. curve fractal of joined truncated tetrahedron.
70. Triakis tetrahedron
E.T. curve fractal of triakis tetrahedron.
71. Joined truncated dodecahedron
E.T. curve fractal of joined truncated dodecahedron.
72. Biscribed orthokis propellor cube
E.T. curve fractal of biscribed orthokis propellor cube.
73. Biscribed orthotruncated propellor octahedron
E.T. curve fractal of biscribed orthotruncated propellor octahedron.
74. Szilassi toroid
E.T. curve fractal of Szilassi toroid.
75. Heptagonal dodecahedron
E.T. curve fractal of heptagonal dodecahedron.
76. Heptagonal dodecahedron
E.T. curve fractal of heptagonal dodecahedron.
77. Hexagonal toroid
E.T. curve fractal of hexagonal toroid.
78. Hexagonal toroid
E.T. curve fractal of hexagonal toroid.
79. Hexagonal toroid
E.T. curve fractal of hexagonal toroid.
80. Regular map
E.T. curve fractal of regular map.
81. Regular map
E.T. curve fractal of regular map.
82. Regular map
E.T. curve fractal of regular map.
83. Regular map
E.T. curve fractal of regular map.
84. Regular map
E.T. curve fractal of regular map.
85. Regular map
E.T. curve fractal of regular map.
86. Regular map
E.T. curve fractal of regular map.
87. Regular map
E.T. curve fractal of regular map.
88. Regular map
E.T. curve fractal of regular map.
89. Great dodecahemidodecacron
E.T. curve fractal of great dodecahemidodecacron.
E.T. curve fractals with polyhedra: 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., "E.T. curve fractals with polyhedra: visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/fractalcurves/et/>, February 2026.
References:
Ventrella, Jeffrey. “Fractal curves”. http://fractalcurves.com/
Weisstein, Eric W. “Uniform Polyhedron.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/UniformPolyhedron.html
McCooey, D. I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/