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Proceedings of CAD'14, 2014, 4-6
Filling the Empty Spaces of the Sierpinski Tetrahedron to Create a 3D Puzzle

Dina Rochman, Sergio Vázquez, Universidad Autónoma Metropolitana, Cuajimalpa

Abstract. Waclaw Sierpinski introduced in 1919 a fractal called Sierpinski triangle. This fractal was developed by Sierpinski from the interaction of an equilateral triangle, where the interaction n=0 is the area of the equilateral triangle of side L, the interaction n=1 is the midpoint of side L, i.e.  L/2 , the interaction n=2 is where each of the triangles has a length  L/4 , and so on. At each interaction the central triangles are extracted leaving empty spaces, and the filled triangles are connected by the vertices. The Sierpinski tetrahedron is the three-dimensional shape of the Sierpinski triangle and is used the same procedure for its construction, but the difference is that in the empty spaces in the Sierpinski tetrahedron we found equal irregular shapes of different sizes. This project stems from the idea of filling, with tetrahedral dimension  L/4 , the empty spaces of Sierpinski tetrahedron in its second stage, i.e. in the n=2 interaction to build a 3D puzzle using the following methodology: (1) development of the Sierpinski tetrahedron in its second stage; (2) analysis of unions and intersections of the tetrahedrons, (3) generation of the modules, and (4) assembly of the 3D Puzzle. The purpose of this paper is to present the method used to fill, with tetrahedrons of dimension  L/4 , the empty spaces of the Sierpinski tetrahedron. And the aim of this research is to create a 3D puzzle using modules that bind and / or intersect each other.

Keywords. Sierpinski tetrahedron, puzzle

DOI: 10.14733/cadconfP.2014.4-6