On critical sets of convex polyhedra (Q760010)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On critical sets of convex polyhedra |
scientific article; zbMATH DE number 3883110
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On critical sets of convex polyhedra |
scientific article; zbMATH DE number 3883110 |
Statements
On critical sets of convex polyhedra (English)
0 references
1985
0 references
The critical set of a convex body \(S\subset E^ n\) is defined as the set \(C(S)=\{c\in S:f(S;c,\lambda (S))\subset S\},\) where \(\lambda\) (S) is a measure of symmetry of S which goes back to H. Minkowski (1897), and \(f(S;c,\lambda)=(1+\lambda)c-\lambda S.\) In this paper it is proved that every polyhedron in \(E^ n\) is the critical set of some other polyhedron.
0 references
critical set
0 references
measure of symmetry
0 references
convex polyhedron
0 references
critical point
0 references
carrier plane
0 references
facet
0 references
connected manifold
0 references
