Tilings of the sphere with right triangles. II: The , subfamily.
Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Diane M. Donovan, James G. Lefevre, Thomas A. McCourt, Nicholas J. Cavenagh (2012)
Commentationes Mathematicae Universitatis Carolinae
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We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for...
Tomohide Hashiba, Yuta Nakagawa, Toshiyuki Yamauchi, Hiroshi Matsui, Satoshi Hashiba, Daisuke Minematsu, Munetoshi Sakaguchi, Ryohei Miyadera (2007)
Visual Mathematics
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Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Broughton, S.Allen, Haney, Dawn M., McKeough, Lori T., Smith Mayfield, Brandy (2000)
The New York Journal of Mathematics [electronic only]
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Dawson, Robert J.Macg., Doyle, Blair (2007)
The Electronic Journal of Combinatorics [electronic only]
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Čerin, Z. (1997)
Mathematica Pannonica
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Fevens, Thomas, Hernandez, Antonio, Mesa, Antonio, Morin, Patrick, Soss, Michael, Toussaint, Godfried (2001)
Beiträge zur Algebra und Geometrie
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Paulus Gerdes (2003)
Visual Mathematics
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Mark Keil, J, Vassilev, Tzvetalin (2010)
Serdica Journal of Computing
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* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005. We consider sets of points in the two-dimensional Euclidean plane. For a planar point set in general position, i.e. no three points collinear, a triangulation is a maximal set of non-intersecting straight line segments with vertices in the given points. These segments, called edges, subdivide the convex hull of the set into triangular regions called...