An InfinitePlane in 3D:

Different styles applied to an infinite plane:

Determine if points belong to a given infinite plane:

Find the plane in which a triangle is embedded:

InfinitePlane can use the same parametrization as Triangle:

Find the plane in which a polygon is embedded:

To find the plane, take the first three points (or any three points not on a line):

The tangent plane to a parametric surface f[u,v] is given by InfinitePlane[f[u,v],{∂_uf[u,v],∂_vf[u,v]}]. Find the tangent plane to the parametric surface :

Find the tangent plane to the surface :

Find the intersection points of a sphere, a plane, and a surface defined by :

Visualize intersection points:

Partition space in a BubbleChart:

Combine the graphics:

Visualize a reflection plane:

Define a reflection plane:

Define a ReflectionTransform using a point on the plane and its normal vector:

Visualize the reflection of a unit cube about the plane:

InfinitePlane[{p₁,p₂,p₃}] is equivalent to InfinitePlane[p₁,{p₂-p₁,p₃-p₁}]:

InfinitePlane[p,{v₁,v₂}] is equivalent to Hyperplane[Cross[v₁,v₂],p] in 3D:

ParametricRegion can represent any InfinitePlane:

ImplicitRegion can represent any InfinitePlane:

InfinitePlane is a special case of ConicHullRegion:

Any InfinitePlane can be represented as a union of two HalfPlane regions:

A random collection of planes:

Sweep an infinite plane around an axis: