🚀 go-pugleaf

Some usual definitions (just to avoid any ambiguity):

	Let k+1 points in R^n be said to be in "general position" if 
	they lie on no (k-1)-dimensional plane.

	Let a subset S of R^n be called a "k-simplex" if it is the convex 
	hull of k+1 points in R^n in general position.  
	
	The k+1 points are the "vertices" of S. 

	A "face" of S is defined as the convex hull of a subset of the vertices.

	Define a compact subset X of R^n to be "triangulated" if X is expressed 
	as the union of finitely many simplices whose pairwise intersection 
	is a common face, or empty.
Now:
Let M be the closure of a bounded open subset of 3-space, and assume that 
the boundary of M consists of a finite number of connected components N(i).  

Assume that each of these N(i) is a compact triangulated surface 
(without boundary).  Call this the "boundary triangulation." 

QUESTION:  Is it necessarily true that M can be triangulated in such 
a way that the restriction of this triangulation to the boundary of M 
is the given boundary triangulation?  

It is easy to see that this is true if M is convex, but what if it isn't?

--Dan Asimov
asimov@nas.nasa.gov

Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799