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
Dragon of Eve fractals with polyhedra
Dragon of Eve curve was discovered by Jeffrey Ventrella in the 1980s, named after Jeffrey’s mother’s art teacher. One way that the Dragon of Eve is different than the classic Dragon Curve is that it has varying lengths in its segments, owing to the fact that the middle segment in the generator has length equal to √2, while the other segments have length 1.
This work shows Dragon of Eve fractals with polyhedra, modeled for visualization in Virtual Reality.
3D models
1. Tetrahedron
Applying the construction principle of the dragon of Eve curve with the tetrahedron, we obtain an tetrahedron dragon of Eve fractal. In the first order of construction of the fractal, we construct three new tetrahedra corresponding to one original polyhedron. In this example, we have solid representations in orders from 0 to 7.
2. Cube
Cube dragon of Eve fractal.
3. Dodecahedron
Dodecahedron dragon of Eve fractal.
4. Icosahedron
Icosahedron dragon of Eve fractal.
5. Octahedron
Octahedron dragon of Eve fractal.
6. Great dodecahedron
Great dodecahedron dragon of Eve fractal.
7. Tetrakis hexahedron
Tetrakis hexahedron dragon of Eve fractal.
8. Great icosahedron
Great icosahedron dragon of Eve fractal.
9. Great triakis icosahedron
Great triakis icosahedron dragon of Eve fractal.
10. Escher solid
Escher solid dragon of Eve fractal.
11. Small stellated dodecahedron
Small stellated dodecahedron dragon of Eve fractal.
12. Great stellated dodecahedron
Great stellated dodecahedron dragon of Eve fractal.
13. Cuboctahedron
Cuboctahedron dragon of Eve fractal.
14. Snub Cube
Snub Cube dragon of Eve fractal.
15. Truncated icosahedron
Truncated icosahedron dragon of Eve fractal.
16. Snub dodecahedron
Snub dodecahedron dragon of Eve fractal.
17. Tetrahemihexahedron
Tetrahemihexahedron dragon of Eve fractal.
18. Tetrahemihexacron
Tetrahemihexacron dragon of Eve fractal.
19. Hexahemioctacron
Hexahemioctacron dragon of Eve fractal.
20. Small Icosihemidodecacron
Small Icosihemidodecacron dragon of Eve fractal.
21. Small dodecahemicosahedron
Small dodecahemicosahedron dragon of Eve fractal.
22. Great Dodecahemicosahedron
Great Dodecahemicosahedron dragon of Eve fractal.
23. Stella Octangula
Stella Octangula dragon of Eve fractal.
24. Concave dodecahedron
Concave dodecahedron dragon of Eve fractal.
25. Jessens Orthogonal Icosahedron
Jessens Orthogonal Icosahedron dragon of Eve fractal.
26. Dyakis dodecahedron
Dyakis dodecahedron dragon of Eve fractal.
27. Small hexacronic icositetrahedron
Small hexacronic icositetrahedron dragon of Eve fractal.
28. Great hexacronic icositetrahedron
Great hexacronic icositetrahedron dragon of Eve fractal.
29. Small icosicosidodecahedron
Small icosicosidodecahedronn dragon of Eve fractal.
30. Dodecadodecahedron
Dodecadodecahedron dragon of Eve fractal.
31. Medial rhombic triacontahedron
Medial rhombic triacontahedron dragon of Eve fractal.
32. Medial triambic icosahedron
Medial triambic icosahedron dragon of Eve fractal.
33. Small ditrigonal dodecacronic hexecontahedron
Small ditrigonal dodecacronic hexecontahedron dragon of Eve fractal.
34. Great triambic icosahedron
Great triambic icosahedron dragon of Eve fractal.
35. Great cubicuboctahedron
Great cubicuboctahedron dragon of Eve fractal.
36. Uniform great rhombicuboctahedron
Uniform great rhombicuboctahedron dragon of Eve fractal.
37. Great rhombihexahedron
Great rhombihexahedron dragon of Eve fractal.
38. Small rhombihexacron
Small rhombihexacron dragon of Eve fractal.
39. Great rhombihexacron
Great rhombihexacron dragon of Eve fractal.
40. Small Dodecicosacron
Small Dodecicosacron dragon of Eve fractal.
41. Small dodecicosahedron
Small dodecicosahedron dragon of Eve fractal.
42. Rhombicosahedron
Rhombicosahedron dragon of Eve fractal.
43. Rhombicosacron
Rhombicosacron dragon of Eve fractal.
44. Cubitruncated Cuboctahedron
Cubitruncated Cuboctahedron dragon of Eve fractal.
45. Tetradyakis hexahedron
Tetradyakis hexahedron dragon of Eve fractal.
46. Great triakis octahedron
Great triakis octahedron dragon of Eve fractal.
47. Great truncated cuboctahedron
Great truncated cuboctahedron dragon of Eve fractal.
48. Great disdyakis dodecahedron
Great disdyakis dodecahedron dragon of Eve fractal.
49. Truncated great dodecahedron
Truncated great dodecahedron dragon of Eve fractal.
50. Small stellapentakis dodecahedron
Small stellapentakis dodecahedron dragon of Eve fractal.
51. Tridyakis icosahedron
Tridyakis icosahedron dragon of Eve fractal.
52. Truncated great icosahedron
Truncated great icosahedron dragon of Eve fractal.
53. Great stellapentakis dodecahedron
Great stellapentakis dodecahedron dragon of Eve fractal.
54. Medial disdyakis triacontahedron
Medial disdyakis triacontahedron dragon of Eve fractal.
55. Great triakis icosahedron
Great triakis icosahedron dragon of Eve fractal.
56. Great disdyakis triacontahedron
Great disdyakis triacontahedron dragon of Eve fractal.
57. Joined truncated cube
Joined truncated cube dragon of Eve fractal.
58. Chamfered octahedron
Chamfered octahedron dragon of Eve fractal.
59. Rhombic dodecahedron
Rhombic dodecahedron dragon of Eve fractal.
60. Triakis octahedron
Triakis octahedron dragon of Eve fractal.
61. Deltoidal icositetrahedron
Deltoidal icositetrahedron dragon of Eve fractal.
62. Pentagonal icositetrahedron
Pentagonal icositetrahedron dragon of Eve fractal.
63. Disdyakis dodecahedron
Disdyakis dodecahedron dragon of Eve fractal.
64. Icosidodecahedron
Icosidodecahedron dragon of Eve fractal.
65. Rhombicuboctahedron
Rhombicuboctahedron dragon of Eve fractal.
66. Truncated tetrahedron
Truncated tetrahedron dragon of Eve fractal.
67. Hendecagonal dodecahedron
Hendecagonal dodecahedron dragon of Eve fractal.
68. Klein map
Klein map dragon of Eve fractal.
69. Joined truncated tetrahedron
Joined truncated tetrahedron dragon of Eve fractal.
70. Triakis tetrahedron
Triakis tetrahedron dragon of Eve fractal.
71. Joined truncated dodecahedron
Joined truncated dodecahedron dragon of Eve fractal.
72. Biscribed orthokis propellor cube
Biscribed orthokis propellor cube dragon of Eve fractal.
73. Biscribed orthotruncated propellor octahedron
Biscribed orthotruncated propellor octahedron dragon of Eve fractal.
74. Szilassi toroid
Szilassi toroid dragon of Eve fractal.
75. Heptagonal dodecahedron
Heptagonal dodecahedron dragon of Eve fractal.
76. Heptagonal dodecahedron
Heptagonal dodecahedron dragon of Eve fractal.
77. Hexagonal toroid
Hexagonal toroid dragon of Eve fractal.
78. Hexagonal toroid
Hexagonal toroid dragon of Eve fractal.
79. Hexagonal toroid
Hexagonal toroid dragon of Eve fractal.
80. Regular map
Regular map dragon of Eve fractal.
81. Regular map
Regular map dragon of Eve fractal.
82. Regular map
Regular map dragon of Eve fractal.
83. Regular map
Regular map dragon of Eve fractal.
84. Regular map
Regular map dragon of Eve fractal.
85. Regular map
Regular map dragon of Eve fractal.
86. Regular map
Regular map dragon of Eve fractal.
87. Regular map
Regular map dragon of Eve fractal.
88. Regular map
Regular map dragon of Eve fractal.
89. Great dodecahemidodecacron
Great dodecahemidodecacron dragon of Eve fractal.
Dragon of Eve 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., "Dragon of Eve fractals with polyhedra: visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/fractalcurves/dragoneve/>, 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/