Parallel redrawing
In geometric graph theory, and the theory of structural rigidity, a parallel redrawing of a graph drawing with straight edges in the Euclidean plane or higher-dimensional Euclidean space is another dr
Grid bracing
In the mathematics of structural rigidity, grid bracing is a problem of adding cross bracing to a square grid to make it into a rigid structure. It can be solved optimally by translating it into a pro
Bricard octahedron
In geometry, a Bricard octahedron is a member of a family of flexible polyhedra constructed by Raoul Bricard in 1897.The overall shape of one of these polyhedron may change in a continuous motion, wit
Rigidity matroid
In the mathematics of structural rigidity, a rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with rigid edges of fixed lengths, embedded into Eucli
Steffen's polyhedron
In geometry, Steffen's polyhedron is a flexible polyhedron discovered (in 1978) by and named after . It is based on the Bricard octahedron, but unlike the Bricard octahedron its surface does not cross
Laman graph
In graph theory, the Laman graphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman graph is a graph on n vertices such that, for
Counting on Frameworks
Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures is an undergraduate-level book on the mathematics of structural rigidity. It was written by Jack E. Graver and published in 20
Carpenter's rule problem
The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices are in
Structural rigidity
In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.
Flexible polyhedron
In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidi
Beckman–Quarles theorem
In geometry, the Beckman–Quarles theorem, named after Frank S. Beckman and Donald A. Quarles Jr., states that if a transformation of the Euclidean plane or a higher-dimensional Euclidean space preserv
Alexandrov's uniqueness theorem
The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between points on their surfaces. It implies that convex
Pseudotriangle
In Euclidean plane geometry, a pseudotriangle (pseudo-triangle) is the simply connected subset of the plane that lies between any three mutually tangent convex sets. A pseudotriangulation (pseudo-tria
Cauchy's theorem (geometry)
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is,