Abstract
A fractal is a figure that has a unique characteristic that will be present in the entire domain of the figure. There are several different types of fractals, some of which are constructed from a simple figure such as a triangle ofplane geometry or a tetrahedron of spatial geometry. From the initial construction of a two-dimensional fractal starting with an equilateral triangle and using Napoleon's Theorem, in this article, we present a construction of a new three-dimensional fractal using ideas similar to Napoleon's Theorem in a tetrahedron. Using concepts of plane and spatial geometry, this fractal can be built from a regular tetrahedron, and from the midpoints of its edges a new tetrahedron with a 1/2 ratio side is built in relation to the initial tetrahedron. After this construction, the characteristics of the infinite application fractal are studied, such as the sum of the surface areas and the total volume of the formed figure.
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