Addition and Decomposition of Polytopes

  • Branko Grünbaum
Part of the Graduate Texts in Mathematics book series (GTM, volume 221)


In this chapter we discuss two methods of ‘adding together’ two polytopes to form a third. The first of these, vector addition or Minkowski addition as it is sometimes called, has already been used in the preceding chapters. The second, called Blaschke addition, will form the topic of section 15.3. One of the main problems is to find criteria for deciding whether a given polytope is decomposable, that is to say, can be expressed as a’ sum’ (in either sense) of other polytopes. In section 15.4 the extension of these results to general convex sets will be discussed, and references given to the relevant literature.


Line Segment Convex Body Supporting Function Steiner Point Convex POLYTOPES 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Branko Grünbaum
    • 1
  1. 1.Department of MathematicsUniversity of Washington, SeattleSeattleUSA

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