Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

polymake: a Framework for Analyzing Convex Polytopes

  • Chapter
Polytopes — Combinatorics and Computation

Part of the book series: DMV Seminar ((OWS,volume 29))

Abstract

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/.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. O. Aichholzer 01play http://www.cis.tu-gran.ac.at/igi/oaich/infoOlpoly.htm1,1999.

  2. N. AmentaComputational geometry softwareIn Goodman and O’Rourke [19], pp. 951–960.

    Google Scholar 

  3. D. Avislrs: A revised implementation of the reverse search vertex enumeration algorithmthis volume, 177–198.

    Google Scholar 

  4. D. Avis lrs Version 3.2ftp://mutt.cs.mcgill.ca/pub/C/lrs.html,Oct14 1998

  5. D. Avis, D. Bremner, and R. SeidelHow good are convex hull algorithms?Comput. Geom. 7 (1997), no. 5–6, 265–301.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  7. M.M. Bayer and C.W. LeeCombinatorial aspects of convex polytopespp. 485–534, In Gruber and Wills [20], 1993.

    Google Scholar 

  8. G. Blind and R. BlindConvex polytopes without triangular facesIsrael J. Math. 71 (1990), no. 2, 129–134.

    MathSciNet  MATH  Google Scholar 

  9. G. Blind and R. Blind Cubical 4-polytopes with few verticesGeom. Dedicata 66 (1997), no. 2, 223–231.

    Article  MathSciNet  Google Scholar 

  10. D. Bremner PolytopeBase Version 0.2 http://www.math.Washington.edu/“bremner/PolytopeBase Mar 4, 1999.

  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. T.H. Cormen, C.E. Leiserson, and R.L. RivestIntroduction to algorithmsMIT Press, 1990.

    Google Scholar 

  13. H.S.M. CoxeterRegular polytopesDover, 1973.

    Google Scholar 

  14. H. EdelsbrunnerAlgorithms in combinatorial geometrySpringer, 1987.

    Google Scholar 

  15. C.Young et alPOV-Ray: Persistence Of Vision, Version 3.1, http://www.povray.org, 1999.

  16. F.J. Brandenburg et al Graphlet, Version 5.0, http://www.fmi.uni-passau.de/Graphlet Jan 11, 1999.

  17. K. Fukuda cddplus, Version 0.76a, http://www.ifor.math.ethz.ch Jun 8,1999.

  18. K. Fukuda and A. ProdonDouble description method revisitedLNCS, vol. 1120, 1996.

    Google Scholar 

  19. J.E. Goodman and J. O’Rourke (eds.)Handbook of discrete and computational geometryCRC Press, 1997.

    Google Scholar 

  20. P.M. Gruber and J.M. Wills (eds.)Handbook of convex geometryNorth-Holland, 1993.

    Google Scholar 

  21. J.E. HumphreysReflection groups and Coxeter groupsCambridge Univ. Press, 1992, corrected paper-back ed.

    MATH  Google Scholar 

  22. M. JoswigReconstructing a non-simple polytope from its graphthis Volume, 167–176.

    Google Scholar 

  23. M. Joswig and G.M. ZieglerNeighborly cubical polytopesDiscrete Comput. Geometry (to appear), math.CO/9812033.

    Google Scholar 

  24. G. KalaiLinear programming the simplex algorithm and simple polytopesMath. Program. Ser. B 79 (1997), 217–233.

    Google Scholar 

  25. D.E. KnuthThe art of computer programming I. Fundamental algorithms3rd ed., Addison-Wesley, 1997.

    Google Scholar 

  26. D.E. Knuth The art of computer programming III. Sorting and searching 2nd ed., Addison-Wesley, 1997.

    Google Scholar 

  27. S. Levy, T. Münzner, and M. Phillips, Geomview, Version 1.6.1, http://www.geom.umn.edu/software/geomview/Oct 30, 1997.

  28. D.R. Musser and A. SainiSTL tutorial and reference guideAddison-Wesley, 1996.

    Google Scholar 

  29. J. Rambau TOPCOM, Version 0.2.0, http://www.zib.de/rambau/topcom.html Jul 28,1999.

  30. J. Richter-Gebert and U.H. KortenkampThe interactive geometry software CinderellaSpringer, 1999.

    Google Scholar 

  31. B. StroustrupThe C++ programming languageAddison-Wesley, 1997, 3rd ed.

    Google Scholar 

  32. L. Wall, T. Christiansen, and R.L. SchwartzProgramming PerlO’Reilly, 1996, 2nd ed.

    Google Scholar 

  33. G.M. ZieglerLectures on polytopesSpringer, 1998, 2nd ed.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, MA 7-1, Technische Universität Berlin, Straße des 17 Juni 136, Berlin, 10623, Germany

    Ewgenij Gawrilow & Michael Joswig

Authors
  1. Ewgenij Gawrilow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Joswig
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, The Hebrew University, Givat Ram, 91904, Jerusalem, Israel

    Gil Kalai

  2. Fachbereich Mathematik MA 7-1, Technische Universität Berlin, Strasse des 17. Juni 135, D-10623, Berlin, Germany

    Günter M. Ziegler

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Basel AG

About this chapter

Cite this chapter

Gawrilow, E., Joswig, M. (2000). polymake: a Framework for Analyzing Convex Polytopes. In: Kalai, G., Ziegler, G.M. (eds) Polytopes — Combinatorics and Computation. DMV Seminar, vol 29. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8438-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8438-9_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-6351-2

  • Online ISBN: 978-3-0348-8438-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation