Special treatment of symmetric polyhedron and polyhedral cone

[blegat]

The fact that a polyhedron is symmetric and/or homogeneous can be determined only with type information if we add the following elements

struct HomHyperPlane{N, T, AT}
    a::AT # ⟨a, x⟩ = 0
end
struct HomHalfSpace{N, T, AT}
    a::AT # ⟨a, x⟩ ≤ 0
end
struct SymHalfSpace{N, T, AT}
    a::AT # -β ≤ ⟨a, x⟩ ≤ β
    β::T
end
struct SymPoint{N, T, AT}
    a::AT # convexhull(-a, a)
end

We would have the following

	Polyhedron	Symmetric	Homogeneous	Linear
Symmetric		Yes		Yes
Homogeneous			Yes	Yes
H-rep
hyperplanetype	HyperPlane	HomHyperPlane	HomHyperPlane	HomHyperPlane
halfspacetype	HalfSpace	SymHalfSpace	HomHalfSpace
V-rep
pointtype	AbstractVector	SymPoint
linetype	Line	Line	Line	Line
raytype	Ray		Ray

The advantage of encoding symmetric and/or homogeneity with a type isn't only efficiency but also accuracy. Roundoff error might make symmetry disappear while it was present in the data at the beginning.
When constructing a representation, e.g. with hrep or vrep, the type of the representation will be determined in a type-stable way.

Two additional category exist but they are different as they are not type-inferrable from both representation:

	Polyhedron	Polytope
Bounded		Yes
V-rep
pointtype	AbstractVector	AbstractVector
linetype	Line
raytype	Ray

	Polyhedron	Affine
Affine		Yes
H-rep
hyperplanetype	HyperPlane	HyperPlane
halfspacetype	HalfSpace