Name
Abstract | ||
|---|---|---|
AbstractA 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 locally 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 any simple and standard ball-polyhedron is locally rigid with respect to its inner dihedral angles. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s00454-012-9480-y | Periodicals |
Keywords | Field | DocType |
Ball-polyhedron,Dual ball-polyhedron,Truncated Delaunay complex,(Infinitesimally) Rigid polyhedron,Rigid ball-polyhedron | Topology,Goldberg polyhedron,Combinatorics,Vertex (geometry),Polyhedron,Ball (bearing),Flexible polyhedron,Euclidean geometry,Congruence (geometry),Dihedral angle,Mathematics | Journal |
Volume | Issue | ISSN |
49 | 2 | 0179-5376 |
Citations | PageRank | References |
1 | 0.41 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Károly Bezdek | 1 | 39 | 14.90 |
| Marton Naszodi | 2 | 21 | 7.87 |