polymake: a Framework for Analyzing Convex Polytopes

  • Ewgenij Gawrilow
  • Michael Joswig
Part of the DMV Seminar book series (OWS, volume 29)


polymake is a software tool designed for the algorithmic treatment of polytopes and polyhedra. We give an overview of the functionality as well as of the structure. This paper can be seen as a first approximation to a polymake handbook.

The tutorial starts with the very basics and ends up with a few polymake applications to research problems. Then we present the main features of the system including the interfaces to other software products. polymake is free software; it is available on the Internet at http://www.math.tu-berlin.de/diskregeom/polymaka/.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
  2. [2]
    N. AmentaComputational geometry softwareIn Goodman and O’Rourke [19], pp. 951–960.Google Scholar
  3. [3]
    D. Avislrs: A revised implementation of the reverse search vertex enumeration algorithmthis volume, 177–198.Google Scholar
  4. [4]
    D. Avis lrs Version 3.2ftp://mutt.cs.mcgill.ca/pub/C/lrs.html,Oct14 1998
  5. [5]
    D. Avis, D. Bremner, and R. SeidelHow good are convex hull algorithms?Comput. Geom. 7 (1997), no. 5–6, 265–301.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    D. Avis and K. FukudaA pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra.Discrete Comput. Geom. 8 (1992), no. 3, 295–313.MathSciNetGoogle Scholar
  7. [7]
    M.M. Bayer and C.W. LeeCombinatorial aspects of convex polytopespp. 485–534, In Gruber and Wills [20], 1993.Google Scholar
  8. [8]
    G. Blind and R. BlindConvex polytopes without triangular facesIsrael J. Math. 71 (1990), no. 2, 129–134.MathSciNetMATHGoogle Scholar
  9. [9]
    G. Blind and R. Blind Cubical 4-polytopes with few verticesGeom. Dedicata 66 (1997), no. 2, 223–231.MathSciNetCrossRefGoogle Scholar
  10. [10]
    D. Bremner PolytopeBase Version 0.2 http://www.math.Washington.edu/“bremner/PolytopeBase Mar 4, 1999.
  11. [11]
    T. Christof and A. Loebel PORTA: POlyhedron Representation Transformation Algorithm, Version 1.3.2, http://www.iwr.uni-heidelberg.de/iwr/comopt/soft Nov 24, 1998.
  12. [12]
    T.H. Cormen, C.E. Leiserson, and R.L. RivestIntroduction to algorithmsMIT Press, 1990.Google Scholar
  13. [13]
    H.S.M. CoxeterRegular polytopesDover, 1973.Google Scholar
  14. [14]
    H. EdelsbrunnerAlgorithms in combinatorial geometrySpringer, 1987.Google Scholar
  15. [15]
    C.Young et alPOV-Ray: Persistence Of Vision, Version 3.1, http://www.povray.org, 1999.
  16. [16]
    F.J. Brandenburg et al Graphlet, Version 5.0, http://www.fmi.uni-passau.de/Graphlet Jan 11, 1999.
  17. [17]
    K. Fukuda cddplus, Version 0.76a, http://www.ifor.math.ethz.ch Jun 8,1999.
  18. [18]
    K. Fukuda and A. ProdonDouble description method revisitedLNCS, vol. 1120, 1996.Google Scholar
  19. [19]
    J.E. Goodman and J. O’Rourke (eds.)Handbook of discrete and computational geometryCRC Press, 1997.Google Scholar
  20. [20]
    P.M. Gruber and J.M. Wills (eds.)Handbook of convex geometryNorth-Holland, 1993.Google Scholar
  21. [21]
    J.E. HumphreysReflection groups and Coxeter groupsCambridge Univ. Press, 1992, corrected paper-back ed.MATHGoogle Scholar
  22. [22]
    M. JoswigReconstructing a non-simple polytope from its graphthis Volume, 167–176.Google Scholar
  23. [23]
    M. Joswig and G.M. ZieglerNeighborly cubical polytopesDiscrete Comput. Geometry (to appear), math.CO/9812033.Google Scholar
  24. [24]
    G. KalaiLinear programming the simplex algorithm and simple polytopesMath. Program. Ser. B 79 (1997), 217–233.Google Scholar
  25. [25]
    D.E. KnuthThe art of computer programming I. Fundamental algorithms3rd ed., Addison-Wesley, 1997.Google Scholar
  26. [26]
    D.E. Knuth The art of computer programming III. Sorting and searching 2nd ed., Addison-Wesley, 1997.Google Scholar
  27. [27]
    S. Levy, T. Münzner, and M. Phillips, Geomview, Version 1.6.1, http://www.geom.umn.edu/software/geomview/Oct 30, 1997.
  28. [28]
    D.R. Musser and A. SainiSTL tutorial and reference guideAddison-Wesley, 1996.Google Scholar
  29. [29]
    J. Rambau TOPCOM, Version 0.2.0, http://www.zib.de/rambau/topcom.html Jul 28,1999.
  30. [30]
    J. Richter-Gebert and U.H. KortenkampThe interactive geometry software CinderellaSpringer, 1999.Google Scholar
  31. [31]
    B. StroustrupThe C++ programming languageAddison-Wesley, 1997, 3rd ed.Google Scholar
  32. [32]
    L. Wall, T. Christiansen, and R.L. SchwartzProgramming PerlO’Reilly, 1996, 2nd ed.Google Scholar
  33. [33]
    G.M. ZieglerLectures on polytopesSpringer, 1998, 2nd ed.Google Scholar

Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • Ewgenij Gawrilow
    • 1
  • Michael Joswig
    • 1
  1. 1.Fachbereich Mathematik, MA 7-1Technische Universität BerlinBerlinGermany

Personalised recommendations