Finding equal-diameter tetrahedralizations of polyhedra

Original Paper


In this paper we show that every simple polyhedron can be tiled into equal-diameter tetrahedra. Our constructive proof does not give bounds for the number of tetrahedra needed.


Triangulation Tetrahedralization Polyhedron Tetrahedron 

Mathematics Subject Classification



  1. Bezdek, A., Bisztriczky, T.: Finding equal-diameter triangulations in polygons. Beitr Algebra Geom. 56(2), 541–549 (2015)MathSciNetCrossRefMATHGoogle Scholar
  2. De Loera, J., Rambau, J., Santos, F.: Triangulations, structures for algorithms and applications, algorithms and computation in mathematics, vol. 25. Springer, Berlin (2010)Google Scholar
  3. Monsky, P.: On dividing a square into triangles. Am. Math. Mon. 77, 161–164 (1970)MathSciNetCrossRefMATHGoogle Scholar
  4. Zamfirescu, C.T.: Survey of two-dimensional acute triangulations. Discrete Math. 313(1), 135–149 (2013)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Managing Editors 2017

Authors and Affiliations

  1. 1.Ybl Faculty of Architecture and Civil EngineeringSzent István UniversityBudapestHungary

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