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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bezdek, A., Bisztriczky, T.: Finding equal-diameter triangulations in polygons. Beitr Algebra Geom. 56(2), 541–549 (2015)
De Loera, J., Rambau, J., Santos, F.: Triangulations, structures for algorithms and applications, algorithms and computation in mathematics, vol. 25. Springer, Berlin (2010)
Monsky, P.: On dividing a square into triangles. Am. Math. Mon. 77, 161–164 (1970)
Zamfirescu, C.T.: Survey of two-dimensional acute triangulations. Discrete Math. 313(1), 135–149 (2013)
About this article
Cite this article
Joós, A. Finding equal-diameter tetrahedralizations of polyhedra. Beitr Algebra Geom 58, 679–698 (2017). https://doi.org/10.1007/s13366-017-0344-8
Mathematics Subject Classification