MeshRegion

MeshRegion[{p₁,p₂,…},{mcell₁[{i₁,…}],mcell₂[{j₁,…}],…}]

yields a mesh with cells mcell_j, where coordinates given as integer i are taken to be p_i.

MeshRegion[…,{…,w_i[mcell_i[…]],…}]

yields a mesh with cell properties defined by the symbolic wrapper w_i.

Details and Options

MeshRegion is also known as a simplicial complex or cell complex.
MeshRegion can represent a piecewise linear region of any geometric dimension embedded in dimension 1, 2, or 3.

MeshRegion[…] displays in a notebook as a plot of a mesh region.
MeshRegion is typically created using functions such as DelaunayMesh, DiscretizeGraphics, and DiscretizeRegion.
The region represented by MeshRegion consists of the disjoint union of mesh cells.
MeshRegion has an embedding dimension that is equal to the length of each point p_i and can be found using RegionEmbeddingDimension.
Each cell has a geometric dimension and can be found using RegionDimension.
Possible mesh cells mcell_i and their geometric dimensions:

Tetrahedron, Hexahedron, Pyramid, and Prism can only be used with 3D coordinates.
Point, Line, Triangle, Polygon, Tetrahedron, Hexahedron, Pyramid, Prism, and Simplex all have multi-cell specifications as well.
The following special wrappers w_i can be used for cells:

	Labeled[cell,…]	display the cell with labeling
	Style[cell,…]	show the cell with the specified style
	Property[cell,name->value]	associate the property name->value with cell

Each cell in a MeshRegion is given a unique MeshCellIndex of the form {d,i}, where d is the geometric dimension and i is the index.
For purposes of selecting cells of a MeshRegion, the following cell specifications may be used:

	{d,i}	cell with index i of dimension d
	{d,ispec}	cells with index specification ispec of dimension d
	{dspec,…}	cells of dimensions given by dspec
	h[{i₁,…}]	explicit cell with head h and vertex indices i₁, …
	{c₁,c₂,…}	list of explicit cells c_i

The index specification ispec can have the following form:
i cell index i

{i₁,i₂,…} cells with indices i_k

All all cells

patt cells with indices matching the pattern patt
The dimension specification dspec can have the following form:
d explicit dimension d

All all dimensions from 0 to geometric dimension of region

patt dimensions matching the pattern patt
MeshRegion is always converted to an optimized representation and treated as raw by functions like AtomQ for purposes of pattern matching.
MeshRegion has the same options as Graphics for embedding dimension 2 and the same options as Graphics3D for embedding dimension 3 with the following additions and changes:

MeshCellLabel	Automatic	labels and placement for cells
MeshCellShapeFunction	Automatic	shape functions for cells
MeshCellStyle	Automatic	styles for cells
MeshCellHighlight	{}	list of highlighted cells
MeshCellMarker	0	integer markers for cells
PlotTheme	$PlotTheme	overall theme for the mesh

Possible settings for PlotTheme include common base themes, font features themes, and size features themes.
Mesh features themes affect plot of mesh cells. Themes include:
"Points" 0D cells

"Lines" 1D cells, wireframe

"Polygons" 2D cells
Rendering features themes affect the rendering of meshes. Themes include:

		"SampledPoints"	sampled points from mesh cells
		"SphereAndTube"	points as spheres and lines as tubes
		"SmoothShading"	smooth shading
		"FaceNormals"	normal for each 2D cell
		"LargeMesh"	optimized for large number of cells

Style and other specifications for cells are effectively applied in the order MeshCellStyle, Style, and other wrappers, with later specifications overriding earlier ones.
Label style and other specifications for cell labels are effectively applied in the order MeshCellLabel and Labeled, with later specifications overriding earlier ones.
MeshRegion can be used with functions such as RegionMember, RegionDistance, RegionMeasure, and NIntegrate.