by adding the time-dimension. Higher dimensional meshes are used in niche contexts. One-dimensional meshes are useful as well. A significant category is surface meshes, which are 2D meshes embedded in 3D to represent a curved surface. Duality Dual graphs have several roles in meshing. One can make a polyhedral Voronoi diagram mesh by dualizing a Delaunay triangulation simplicial mesh. One can create a cubical mesh by generating an arrangement of surfaces and dualizing the intersection graph; see spatial twist continuum. Sometimes both the primal mesh and its dual mesh are used in the same simulation; see Hodge star operator. This arises from physics involving divergence and curl (mathematics) operators, such as flux & vorticity or electricity & magnetism, where one variable naturally lives on the primal faces and its counterpart on the dual faces. Mesh type by use Three-dimensional meshes created for finite element analysis need to consist of tetrahedra, pyramids, prisms or hexahedra. Those used for the finite volume method can consist of arbitrary polyhedra. Those used for finite difference methods consist of piecewise structured arrays of hexahedra known as multi-block structured meshes. 4-sided pyramids are useful to conformally connect hexes to tets. 3-sided prisms are used for boundary layers conforming to a tet mesh of the far-interior of the object. Surface meshes are useful in computer graphics where the surfaces of objects reflect light (also subsurface scattering) and a full 3D mesh is not needed. Surface meshes are also used to model thin objects such as sheet metal in auto manufacturing and building exteriors in architecture. High (e.g., 17) dimensional cubical meshes are common in astrophysics and string theory. Mathematical definition and variants What is the precise definition of a mesh? There is not a universally-accepted mathematical description that applies in all contexts. However, some mathematical objects are clearly meshes: a simplicial complex is a mesh composed of simplices. Most polyhedral (e.g. cubical) meshes are conformal, meaning they have the cell structure of a CW complex, a generalization of a simplicial complex. A mesh need not be simplicial because an arbitrary subset of nodes of a cell is not necessarily a cell: e.g., three nodes of a quad does not define a cell. However, two cells intersect at cells: e.g. a quad does not have a node in its interior. The intersection of two cells may be several cells: e.g., two quads may share two edges. An intersection