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In this chapter, the following notions play the essential roles: zonotopes (finite sums of segments), zonoids (limits of zonotopes), projection bodies (zonotopes or zonoids whose support function values present the (n − 1)-dimensional orthogonal projection areas of given n-dimensional convex polytopes or convex bodies), polars of projection bodies, mixed projection bodies and projection maps, centroid bodies, and valuations (for the latter, see also Chapter 11 ).

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Affine Convex Geometry—Part 2

  • 章节

  • 发表日期：

    2025年

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  • Vitor Balestro,
  • Horst Martini,
  • Ralph Teixeira

摘要

In this chapter, the following notions play the essential roles: zonotopes (finite sums of segments), zonoids (limits of zonotopes), projection bodies (zonotopes or zonoids whose support function values present the (n − 1)-dimensional orthogonal projection areas of given n-dimensional convex polytopes or convex bodies), polars of projection bodies, mixed projection bodies and projection maps, centroid bodies, and valuations (for the latter, see also Chapter 11 ).