Mathematics – Metric Geometry
Scientific paper
2011-10-11
European Journal of Combinatorics 27 (2006), 255-268
Mathematics
Metric Geometry
12 pages
Scientific paper
10.1016/j.ejc.2004.08.007
A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ball-polyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ball-polyhedron if its vertex-edge-face structure is a lattice (with respect to containment). To each edge of a ball-polyhedron one can assign an inner dihedral angle and say that the given ball-polyhedron is rigid with respect to its inner dihedral angles if the vertex-edge-face structure of the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron up to congruence locally. The main result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra stating that a simple ball-polyhedron is rigid with respect to its inner dihedral angles if and only if it is a standard ball-polyhedron.
Bezdek Karoly
NaszÓdi MÁrton
No associations
LandOfFree
Rigid ball-polyhedra in Euclidean 3-space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Rigid ball-polyhedra in Euclidean 3-space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigid ball-polyhedra in Euclidean 3-space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-631952