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2011 The Steiner problem on the regular tetrahedron
Kyra Moon, Gina Shero, Denise Halverson
Involve 4(4): 365-404 (2011). DOI: 10.2140/involve.2011.4.365

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.

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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

Information

Received: 14 January 2011; Revised: 22 March 2011; Accepted: 24 March 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1245.51005
MathSciNet: MR2905235
Digital Object Identifier: 10.2140/involve.2011.4.365

Subjects:
Primary: 05C05
Secondary: 51M15

Keywords: length minimization , piecewise-linear surface , regular tetrahedron , Steiner problem

Rights: Copyright © 2011 Mathematical Sciences Publishers

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