Abstract
The only previously published triangulation of then-cube usingo(n!) simplices, due to Sallee, usesO(n −2 n!) simplices. We point out a very simple method of achievingO(ρ n n!) simplices, where ρ<1 is a constant.
Article PDF
Similar content being viewed by others
References
L. J. Billera, R. Cushman, and J. A. Sanders, The Stanley decomposition of the harmonic oscillator,Nederl. Akad. Wetensch. Proc. Ser. A 91 (1988), 375–393.
R. W. Cottle, Minimal triangulations of the 4-cube,Discrete Math. 40 (1982), 25–29.
C. Lee, Triangulating thed-cube, inDiscrete Geometry and Convexity, J. E. Goodman, E. Lutwak, J. Malkevitch, and R. Pollack, eds., New York Academy of Sciences, New York (1985), pp. 205–211.
C. Lee, Some notes on triangulating polytopes, inProc. 3. Kolloquium über Diskrete Geometrie, Institut für Mathematik, Universität Salzburg (1985), pp. 173–181.
P. S. Mara, Triangulations of the Cube, M, S. Thesis, Colorado State University (1972).
J. F. Sallee, A triangulation of then-cube,Discrete Math. 40 (1982), 81–86.
J. F. Sallee, Middle-cut triangulations of then-cube,SIAM J. Algebraic Discrete Methods 5, no. 3 (1984), 407–419.
W. D. Smith, Polytope triangulations ind-space, improving Hadamard's inequality and maximal volumes of regular polytopes in hyperbolicd-space. Manuscript, Princeton, NJ (September 1987).
R. P. Stanley, Decompositions of rational convex polytopes,Ann. Discrete Math. 6 (1980), 333–342.
R. P. Stanley,Enumerative Combinatorics, Vol. I, Wadsworth & Brooks/Cole, Monterey, CA (1986).
M. J. Todd,The Computation of Fixed Points and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 124, Springer-Verlag, Berlin (1976).
B. Von Hohenbalken, How To Simplicially Partition a Polytope, Research Paper No. 79-17, Department of Economics, University of Alberta, Edmonton (1979).
Author information
Authors and Affiliations
Additional information
This research was supported in part by N.S.F. Grant No. DMS-8717795.
Rights and permissions
About this article
Cite this article
Haiman, M. A simple and relatively efficient triangulation of then-cube. Discrete Comput Geom 6, 287–289 (1991). https://doi.org/10.1007/BF02574690
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02574690