Linear Algebra › Section H · The geometry of vector spaces › Topic H.5
Polytopes
Triangles, cubes and pyramids are the familiar members of a family that exists in every dimension. Polytopes are convex hulls of finitely many points, and their corners decide where linear quantities such as cost or profit reach their extremes, the key fact behind linear programming.
In this topic
- Polygons, polyhedra and beyond
- Extreme points
- A polytope is the hull of its corners
- Faces and the two descriptions
- Worked example: vertices from inequalities
- Worked example: linear programming
- Simplices
- Hypercubes and Euler's formula
- Common mistakes to avoid
- Key takeaways
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