Whats the difference between FACES and FACETS of polyhedra?

[konfusus]

hi guys,

I'm encountering serious troubles in understanding a textbook...

"This inequality clearly defines a proper face of Q. Assume now that it is not facet defining for Q"

I'm not a native speaker, and i can't find any proper definition online...

So, could anybody please post them for me?

i'd be so full of thanks

 

[Gene]

Have you looked at
http://web.aanet.com.au/robertw/Glossary.html
------------------
Gene

 

[konfusus]

HEy thanks - that's the kind of page i've been looking for

 

[konfusus]

damn, still not satisfying...

I've meanwhile found another page.

The one u just posted says:

Face
What we call the flat sides of a polyhedron. Each face is a polygon. For example, a cube has square faces.

Facet
A facet of a polyhedron is a polygon whose vertices are all vertices of that polyhedron, although it is generally not a face of that polyhedron.

this one here http://carbon.cudenver.edu/~hgreenbe/glossary/index.php?page=F.html

says:

Face. A convex subset, say S, of a convex set, say C, such that [x, y] in C and [x, y] /\ ri(S) not empty imply x, y are in S. C, itself, is a face of C, and most authors consider the empty set a face. The faces of zero dimension are the extreme points of C. When C is a polyhedron, {x: Ax <= b}, the faces are the subsystems with some inequalities holding with equality: {x: Bx = c, Dx <= d}, where A = [B D] and b = [c' d']'.

Facet. A face of a convex set, not equal to the set, of maximal dimension. If the set is polyhedral, say P = {x: Ax <= b}, where the defining inequalities are irredundant, the facets are in 1-1 correspondence with {x in P: A(i,.)x = b_i} for i such that the equality is not forced – i.e., there exists x in P for which A(i,.)x < b_i.

Who's right?

(actually, imho the second one sounds way more trustworthy..)