Basic Geometric Regions
The Wolfram Language provides a rich collection of basic regions, ranging from simple triangles and infinite lines to general ellipsoids and conic hulls. Many basic regions are also defined for any dimension. Basic regions work just like any other region in the Wolfram Language and can be analyzed, used as input to solvers, or used as a building block to construct more complex regions.
EmptyRegion — an empty region in 
D
FullRegion — a full region in 
D
Interval — an interval in 1D
Point — a point or list of points in 
D
Line — a piecewise linear line in 
D
InfiniteLine — a doubly infinite line in 
D
HalfLine — a half infinite line (or ray) in 
D
SSSTriangle — a side-side-side triangle in 2D
SASTriangle — a side-angle-side triangle in 2D
ASATriangle — an angle-side-angle triangle in 2D
AASTriangle — an angle-angle-side triangle in 2D
Triangle — a triangle in 
D
Rectangle — an axis-aligned rectangle in 2D
Parallelogram — a parallelogram, rhomboid, rhombus, etc. in 2D
RegularPolygon — a regular polygon in 2D
Polygon — a polygon in 2D or 3D
InfinitePlane — a plane in 
D
HalfPlane — a half-plane in 
D
Cube — a filled cube in 3D
Dodecahedron — a filled dodecahedron in 3D
Icosahedron — a filled icosahedron in 3D
Octahedron — a filled octahedron in 3D
Tetrahedron — a filled tetrahedron in 3D
UniformPolyhedron — a uniform polyhedron in 3D
Hexahedron — a filled hexahedron in 3D
Pyramid — a filled pyramid over a quadrilateral in 3D
Prism — a filled triangular prism in 3D
Cuboid — a filled axis-aligned cuboid, box, etc. in 
D
Parallelepiped — a filled parallelepiped, parallelotope, etc. in 
D
Simplex — a simplex in 
D
Hyperplane — a hyperplane in 
D
HalfSpace — a half-space in 
D
AffineSpace — an affine space in 
D
AffineHalfSpace — an affine half-space in 
D
ConicHullRegion — a polyhedral cone in 
D
Circle — a circle, ellipse, or arc in 2D
CircleThrough — circle through specified points
Disk — a disk, filled ellipse, or sector in 2D
DiskSegment — a filled segment of disk or ellipse in 2D
Annulus — the filled region between two concentric circles in 2D
StadiumShape — a filled stadium shape in 2D
Sphere — a spherical shell in 
D given by center and radius
Circumsphere — a sphere in 
D given by 
points (circumscribing the simplex)
Insphere — a sphere in 
D given by n+1 points (inscribed in the simplex)
Ball — a filled ball in 
D given by center and radius
Ellipsoid — a filled ellipsoid in 
D
Cylinder — a filled cylinder given by two points and a radius in 3D
Cone — a filled cone given by two points and a radius in 3D
CapsuleShape — a filled capsule given by two points and radius in 3D
SphericalShell — the filled region between two spheres in 
D
Torus — a torus in 3D
FilledTorus — a filled torus in 3D
Tube — a tube around a line or curve in 3D
HilbertCurve — generate a Hilbert curve in nD
PeanoCurve — generate a Peano curve in 2D
SierpinskiCurve — generate a Sierpiński curve in 2D
KochCurve — generate a Koch curve in 2D
Regions in 1D
Point ▪ Hyperplane ▪ Interval ▪ Line ▪ InfiniteLine ▪ HalfLine ▪ HalfSpace ▪ AffineSpace ▪ AffineHalfSpace ▪ Sphere ▪ Circumsphere ▪ Insphere ▪ Ball
Regions in 2D
Point ▪ Line ▪ Hyperplane ▪ InfiniteLine ▪ HalfLine ▪ Triangle ▪ SSSTriangle ▪ SASTriangle ▪ ASATriangle ▪ AASTriangle ▪ Rectangle ▪ Parallelogram ▪ RegularPolygon ▪ Polygon ▪ InfinitePlane ▪ HalfPlane ▪ HalfSpace ▪ AffineSpace ▪ AffineHalfSpace ▪ Simplex ▪ ConicHullRegion ▪ Circle ▪ CircleThrough ▪ Disk ▪ DiskSegment ▪ Sphere ▪ Circumsphere ▪ Insphere ▪ Ball ▪ Annulus ▪ StadiumShape
Regions in 3D
Point ▪ Line ▪ InfiniteLine ▪ HalfLine ▪ Triangle ▪ Polygon ▪ Hyperplane ▪ InfinitePlane ▪ HalfPlane ▪ HalfSpace ▪ AffineSpace ▪ AffineHalfSpace ▪ ConicHullRegion ▪ Simplex ▪ Cube ▪ Dodecahedron ▪ Icosahedron ▪ Octahedron ▪ Tetrahedron ▪ Cuboid ▪ Parallelepiped ▪ Hexahedron ▪ Prism ▪ Pyramid ▪ Sphere ▪ Circumsphere ▪ Insphere ▪ Ball ▪ Cylinder ▪ Cone ▪ SphericalShell ▪ CapsuleShape ▪ Torus ▪ FilledTorus ▪ Tube
Regions in 
D
Point ▪ Line ▪ InfiniteLine ▪ HalfLine ▪ Triangle ▪ InfinitePlane ▪ HalfPlane ▪ Hyperplane ▪ Simplex ▪ Cuboid ▪ Parallelepiped ▪ HalfSpace ▪ AffineSpace ▪ AffineHalfSpace ▪ ConicHullRegion ▪ Sphere ▪ Circumsphere ▪ Insphere ▪ Ball ▪ Ellipsoid ▪ SphericalShell
Basic Regions from Data
BoundingRegion — basic region bounds from points and regions
RegionFit — basic regions fitted to data