Abstract
The Steiner problem involves finding a shortest path network connecting a specified set of points. In this paper, we examine the Steiner problem for three points on the surface of a regular tetrahedron. We prove several important properties about Steiner minimal trees on a regular tetrahedron. There are infinitely many ways to connect three points on a tetrahedron, so we present a way to eliminate all but a finite number of possible solutions. We provide an algorithm for finding a shortest network connecting three given points on a regular tetrahedron. The solution can be found by direct measurement of the remaining possible Steiner trees.
Citation
Kyra Moon. Gina Shero. Denise Halverson. "The Steiner problem on the regular tetrahedron." Involve 4 (4) 365 - 404, 2011. https://doi.org/10.2140/involve.2011.4.365
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