diff --git a/ext/ManifoldsRecipesBaseExt.jl b/ext/ManifoldsRecipesBaseExt.jl
index 6d9b831124..65068c4553 100644
--- a/ext/ManifoldsRecipesBaseExt.jl
+++ b/ext/ManifoldsRecipesBaseExt.jl
@@ -2,6 +2,7 @@ module ManifoldsRecipesBaseExt
 
 if isdefined(Base, :get_extension)
     using Manifolds
+    using Manifolds: TypeParameter
 
     using Colors: RGBA
     using RecipesBase: @recipe, @series
@@ -9,6 +10,7 @@ else
     # imports need to be relative for Requires.jl-based workflows:
     # https://github.com/JuliaArrays/ArrayInterface.jl/pull/387
     using ..Manifolds
+    using ..Manifolds: TypeParameter
 
     using ..RecipesBase: @recipe, @series
     using ..Colors: RGBA
@@ -24,7 +26,7 @@ SURFACE_RESOLUTION_DEFAULT = 32
 # Plotting Recipe – Poincaré Ball
 #
 @recipe function f(
-    M::Hyperbolic{2},
+    M::Hyperbolic{TypeParameter{Tuple{2}}},
     pts::AbstractVector{P},
     vecs::Union{AbstractVector{T},Nothing}=nothing;
     circle_points=CIRCLE_DEFAULT_PLOT_POINTS,
@@ -87,7 +89,7 @@ end
 # Plotting Recipe – Poincaré Half plane
 #
 @recipe function f(
-    M::Hyperbolic{2},
+    M::Hyperbolic{TypeParameter{Tuple{2}}},
     pts::AbstractVector{P},
     vecs::Union{AbstractVector{T},Nothing}=nothing;
     geodesic_interpolation=-1,
@@ -133,7 +135,7 @@ end
 # Plotting Recipe – Hyperboloid
 #
 @recipe function f(
-    M::Hyperbolic{2},
+    M::Hyperbolic{TypeParameter{Tuple{2}}},
     pts::Union{AbstractVector{P},Nothing}=nothing,
     vecs::Union{AbstractVector{T},Nothing}=nothing;
     geodesic_interpolation=-1,
@@ -229,7 +231,7 @@ end
 # Plotting Recipe – Sphere
 #
 @recipe function f(
-    M::Sphere{2,ℝ},
+    M::Sphere{TypeParameter{Tuple{2}},ℝ},
     pts::Union{AbstractVector{P},Nothing}=nothing,
     vecs::Union{AbstractVector{T},Nothing}=nothing;
     geodesic_interpolation=-1,
diff --git a/src/manifolds/Hyperbolic.jl b/src/manifolds/Hyperbolic.jl
index 9e18b5ec22..bf40bee973 100644
--- a/src/manifolds/Hyperbolic.jl
+++ b/src/manifolds/Hyperbolic.jl
@@ -1,5 +1,5 @@
 @doc raw"""
-    Hyperbolic{N} <: AbstractDecoratorManifold{ℝ}
+    Hyperbolic{T} <: AbstractDecoratorManifold{ℝ}
 
 The hyperbolic space $\mathcal H^n$ represented by $n+1$-Tuples, i.e. embedded in the
 [`Lorentz`](@ref)ian manifold equipped with the [`MinkowskiMetric`](@ref)
@@ -29,13 +29,18 @@ and the Poincaré half space model, see [`PoincareHalfSpacePoint`](@ref) and [`P
 
 # Constructor
 
-    Hyperbolic(n)
+    Hyperbolic(n::Int; parameter::Symbol=:field)
 
 Generate the Hyperbolic manifold of dimension `n`.
 """
-struct Hyperbolic{N} <: AbstractDecoratorManifold{ℝ} end
+struct Hyperbolic{T} <: AbstractDecoratorManifold{ℝ}
+    size::T
+end
 
-Hyperbolic(n::Int) = Hyperbolic{n}()
+function Hyperbolic(n::Int; parameter::Symbol=:field)
+    size = wrap_type_parameter(parameter, (n,))
+    return Hyperbolic{typeof(size)}(size)
+end
 
 function active_traits(f, ::Hyperbolic, args...)
     return merge_traits(IsIsometricEmbeddedManifold(), IsDefaultMetric(MinkowskiMetric()))
@@ -152,7 +157,7 @@ last entry, i.e. $p_n>0$
 check_point(::Hyperbolic, ::Any)
 
 @doc raw"""
-    check_vector(M::Hyperbolic{n}, p, X; kwargs... )
+    check_vector(M::Hyperbolic, p, X; kwargs... )
 
 Check whether `X` is a tangent vector to `p` on the [`Hyperbolic`](@ref) `M`, i.e.
 after [`check_point`](@ref)`(M,p)`, `X` has to be of the same dimension as `p`.
@@ -166,12 +171,13 @@ For a the Poincaré ball as well as the Poincaré half plane model, `X` has to b
 check_vector(::Hyperbolic, ::Any, ::Any)
 
 function check_vector(
-    M::Hyperbolic{N},
+    M::Hyperbolic,
     p,
     X::Union{PoincareBallTVector,PoincareHalfSpaceTVector};
     kwargs...,
-) where {N}
-    return check_point(Euclidean(N), X.value; kwargs...)
+)
+    n = get_n(M)
+    return check_point(Euclidean(n), X.value; kwargs...)
 end
 
 # Define self conversions
@@ -195,7 +201,16 @@ function diagonalizing_projectors(M::Hyperbolic, p, X)
     )
 end
 
-get_embedding(::Hyperbolic{N}) where {N} = Lorentz(N + 1, MinkowskiMetric())
+function get_embedding(::Hyperbolic{TypeParameter{Tuple{n}}}) where {n}
+    return Lorentz(n + 1, MinkowskiMetric(); parameter=:type)
+end
+function get_embedding(M::Hyperbolic{Tuple{Int}})
+    n = get_n(M)
+    return Lorentz(n + 1, MinkowskiMetric())
+end
+
+get_n(::Hyperbolic{TypeParameter{Tuple{n}}}) where {n} = n
+get_n(M::Hyperbolic{Tuple{Int}}) = get_parameter(M.size)[1]
 
 embed(::Hyperbolic, p::AbstractArray) = p
 embed(::Hyperbolic, p::AbstractArray, X::AbstractArray) = X
@@ -297,7 +312,7 @@ end
 
 Return the dimension of the hyperbolic space manifold $\mathcal H^n$, i.e. $\dim(\mathcal H^n) = n$.
 """
-manifold_dimension(::Hyperbolic{N}) where {N} = N
+manifold_dimension(M::Hyperbolic) = get_n(M)
 
 @doc raw"""
     manifold_dimension(M::Hyperbolic)
@@ -342,7 +357,13 @@ the [`Lorentz`](@ref)ian manifold.
 """
 project(::Hyperbolic, ::Any, ::Any)
 
-Base.show(io::IO, ::Hyperbolic{N}) where {N} = print(io, "Hyperbolic($(N))")
+function Base.show(io::IO, ::Hyperbolic{TypeParameter{Tuple{n}}}) where {n}
+    return print(io, "Hyperbolic($(n); parameter=:type)")
+end
+function Base.show(io::IO, M::Hyperbolic{Tuple{Int}})
+    n = get_n(M)
+    return print(io, "Hyperbolic($(n))")
+end
 for T in _HyperbolicTypes
     @eval Base.show(io::IO, p::$T) = print(io, "$($T)($(p.value))")
 end
diff --git a/src/manifolds/HyperbolicHyperboloid.jl b/src/manifolds/HyperbolicHyperboloid.jl
index 4bd14068e7..e465bf35bc 100644
--- a/src/manifolds/HyperbolicHyperboloid.jl
+++ b/src/manifolds/HyperbolicHyperboloid.jl
@@ -1,5 +1,5 @@
 @doc raw"""
-    change_representer(M::Hyperbolic{n}, ::EuclideanMetric, p, X)
+    change_representer(M::Hyperbolic, ::EuclideanMetric, p, X)
 
 Change the Eucliden representer `X` of a cotangent vector at point `p`.
 We only have to correct for the metric, which means that the sign of the last entry changes, since
@@ -262,7 +262,8 @@ function _get_basis(
     return get_basis_orthonormal(M, p, ℝ)
 end
 
-function get_basis_orthonormal(M::Hyperbolic{n}, p, r::RealNumbers) where {n}
+function get_basis_orthonormal(M::Hyperbolic, p, r::RealNumbers)
+    n = get_n(M)
     V = [
         _hyperbolize(M, p, [i == k ? one(eltype(p)) : zero(eltype(p)) for k in 1:n]) for
         i in 1:n
@@ -364,8 +365,8 @@ i.e. $X_{n+1} = \frac{⟨\tilde p, Y⟩}{p_{n+1}}$, where $\tilde p = (p_1,\ldot
 _hyperbolize(::Hyperbolic, p, Y) = vcat(Y, dot(p[1:(end - 1)], Y) / p[end])
 
 @doc raw"""
-    inner(M::Hyperbolic{n}, p, X, Y)
-    inner(M::Hyperbolic{n}, p::HyperboloidPoint, X::HyperboloidTVector, Y::HyperboloidTVector)
+    inner(M::Hyperbolic, p, X, Y)
+    inner(M::Hyperbolic, p::HyperboloidPoint, X::HyperboloidTVector, Y::HyperboloidTVector)
 
 Cmpute the inner product in the Hyperboloid model, i.e. the [`minkowski_metric`](@ref) in
 the embedding. The formula reads
@@ -409,11 +410,12 @@ end
 
 function Random.rand!(
     rng::AbstractRNG,
-    M::Hyperbolic{N},
+    M::Hyperbolic,
     pX;
     vector_at=nothing,
-    σ=one(eltype(pX)),
-) where {N}
+    σ::Real=one(eltype(pX)),
+)
+    N = get_n(M)
     if vector_at === nothing
         a = randn(rng, N)
         f = 1 + σ * abs(randn(rng))
diff --git a/src/manifolds/HyperbolicPoincareBall.jl b/src/manifolds/HyperbolicPoincareBall.jl
index a5252c963e..624ff1a7d1 100644
--- a/src/manifolds/HyperbolicPoincareBall.jl
+++ b/src/manifolds/HyperbolicPoincareBall.jl
@@ -1,5 +1,5 @@
 @doc raw"""
-    change_representer(M::Hyperbolic{n}, ::EuclideanMetric, p::PoincareBallPoint, X::PoincareBallTVector)
+    change_representer(M::Hyperbolic, ::EuclideanMetric, p::PoincareBallPoint, X::PoincareBallTVector)
 
 Since in the metric we have the term `` α = \frac{2}{1-\sum_{i=1}^n p_i^2}`` per element,
 the correction for the gradient reads `` Y = \frac{1}{α^2}X``.
@@ -24,7 +24,7 @@ function change_representer!(
 end
 
 @doc raw"""
-    change_metric(M::Hyperbolic{n}, ::EuclideanMetric, p::PoincareBallPoint, X::PoincareBallTVector)
+    change_metric(M::Hyperbolic, ::EuclideanMetric, p::PoincareBallPoint, X::PoincareBallTVector)
 
 Since in the metric we always have the term `` α = \frac{2}{1-\sum_{i=1}^n p_i^2}`` per element,
 the correction for the metric reads ``Z = \frac{1}{α}X``.
@@ -43,7 +43,7 @@ function change_metric!(
     return Y
 end
 
-function check_point(M::Hyperbolic{N}, p::PoincareBallPoint; kwargs...) where {N}
+function check_point(M::Hyperbolic, p::PoincareBallPoint; kwargs...)
     if !(norm(p.value) < 1)
         return DomainError(
             norm(p.value),
@@ -52,7 +52,8 @@ function check_point(M::Hyperbolic{N}, p::PoincareBallPoint; kwargs...) where {N
     end
 end
 
-function check_size(M::Hyperbolic{N}, p::PoincareBallPoint) where {N}
+function check_size(M::Hyperbolic, p::PoincareBallPoint)
+    N = get_n(M)
     if size(p.value, 1) != N
         !(norm(p.value) < 1)
         return DomainError(
@@ -62,12 +63,8 @@ function check_size(M::Hyperbolic{N}, p::PoincareBallPoint) where {N}
     end
 end
 
-function check_size(
-    M::Hyperbolic{N},
-    p::PoincareBallPoint,
-    X::PoincareBallTVector;
-    kwargs...,
-) where {N}
+function check_size(M::Hyperbolic, p::PoincareBallPoint, X::PoincareBallTVector; kwargs...)
+    N = get_n(M)
     if size(X.value, 1) != N
         return DomainError(
             size(X.value, 1),
@@ -273,12 +270,19 @@ embed(::Hyperbolic, p::PoincareBallPoint) = p.value
 embed!(::Hyperbolic, q, p::PoincareBallPoint) = copyto!(q, p.value)
 embed(::Hyperbolic, p::PoincareBallPoint, X::PoincareBallTVector) = X.value
 embed!(::Hyperbolic, Y, p::PoincareBallPoint, X::PoincareBallTVector) = copyto!(Y, X.value)
-get_embedding(::Hyperbolic{n}, p::PoincareBallPoint) where {n} = Euclidean(n)
+
+function get_embedding(::Hyperbolic{TypeParameter{Tuple{n}}}, ::PoincareBallPoint) where {n}
+    return Euclidean(n; parameter=:type)
+end
+function get_embedding(M::Hyperbolic{Tuple{Int}}, ::PoincareBallPoint)
+    n = get_n(M)
+    return Euclidean(n)
+end
 
 @doc raw"""
     inner(::Hyperbolic, p::PoincareBallPoint, X::PoincareBallTVector, Y::PoincareBallTVector)
 
-Compute the inner producz in the Poincaré ball model. The formula reads
+Compute the inner product in the Poincaré ball model. The formula reads
 ````math
 g_p(X,Y) = \frac{4}{(1-\lVert p \rVert^2)^2}  ⟨X, Y⟩ .
 ````
diff --git a/src/manifolds/HyperbolicPoincareHalfspace.jl b/src/manifolds/HyperbolicPoincareHalfspace.jl
index 973a39b8e7..64ad2ac394 100644
--- a/src/manifolds/HyperbolicPoincareHalfspace.jl
+++ b/src/manifolds/HyperbolicPoincareHalfspace.jl
@@ -1,4 +1,4 @@
-function check_point(M::Hyperbolic{N}, p::PoincareHalfSpacePoint; kwargs...) where {N}
+function check_point(M::Hyperbolic, p::PoincareHalfSpacePoint; kwargs...)
     if !(last(p.value) > 0)
         return DomainError(
             norm(p.value),
@@ -7,7 +7,8 @@ function check_point(M::Hyperbolic{N}, p::PoincareHalfSpacePoint; kwargs...) whe
     end
 end
 
-function check_size(M::Hyperbolic{N}, p::PoincareHalfSpacePoint) where {N}
+function check_size(M::Hyperbolic, p::PoincareHalfSpacePoint)
+    N = get_n(M)
     if size(p.value, 1) != N
         !(norm(p.value) < 1)
         return DomainError(
@@ -18,11 +19,12 @@ function check_size(M::Hyperbolic{N}, p::PoincareHalfSpacePoint) where {N}
 end
 
 function check_size(
-    M::Hyperbolic{N},
+    M::Hyperbolic,
     p::PoincareHalfSpacePoint,
     X::PoincareHalfSpaceTVector;
     kwargs...,
-) where {N}
+)
+    N = get_n(M)
     if size(X.value, 1) != N
         return DomainError(
             size(X.value, 1),
@@ -210,11 +212,21 @@ embed(::Hyperbolic, p::PoincareHalfSpacePoint, X::PoincareHalfSpaceTVector) = X.
 function embed!(::Hyperbolic, Y, p::PoincareHalfSpacePoint, X::PoincareHalfSpaceTVector)
     return copyto!(Y, X.value)
 end
-get_embedding(::Hyperbolic{n}, p::PoincareHalfSpacePoint) where {n} = Euclidean(n)
+
+function get_embedding(
+    ::Hyperbolic{TypeParameter{Tuple{n}}},
+    ::PoincareHalfSpacePoint,
+) where {n}
+    return Euclidean(n; parameter=:type)
+end
+function get_embedding(M::Hyperbolic{Tuple{Int}}, ::PoincareHalfSpacePoint)
+    n = get_n(M)
+    return Euclidean(n)
+end
 
 @doc raw"""
     inner(
-        ::Hyperbolic{n},
+        ::Hyperbolic,
         p::PoincareHalfSpacePoint,
         X::PoincareHalfSpaceTVector,
         Y::PoincareHalfSpaceTVector
diff --git a/src/manifolds/Lorentz.jl b/src/manifolds/Lorentz.jl
index 831d4fee68..95d1d78bb1 100644
--- a/src/manifolds/Lorentz.jl
+++ b/src/manifolds/Lorentz.jl
@@ -16,7 +16,7 @@ see [`minkowski_metric`](@ref) for the formula.
 struct MinkowskiMetric <: LorentzMetric end
 
 @doc raw"""
-    Lorentz{N} = MetricManifold{Euclidean{N,ℝ},LorentzMetric}
+    Lorentz{T} = MetricManifold{Euclidean{T,ℝ},LorentzMetric}
 
 The Lorentz manifold (or Lorentzian) is a pseudo-Riemannian manifold.
 
diff --git a/test/recipes.jl b/test/recipes.jl
index f595fa3044..831dcbda67 100644
--- a/test/recipes.jl
+++ b/test/recipes.jl
@@ -10,7 +10,7 @@ include("utils.jl")
         ENV["GKSwstype"] = "100"
         gr()
         #        function Hyp2PB_plot()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         p2 = convert.(Ref(PoincareBallPoint), p)
         #            return
@@ -19,7 +19,7 @@ include("utils.jl")
         #       @plottest Hyp2PB_plot joinpath(references_folder, "Hyp2PBPlot.png") false
 
         #       function Hyp2PB_plot_geo()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         p2 = convert.(Ref(PoincareBallPoint), p)
         #           return
@@ -28,7 +28,7 @@ include("utils.jl")
         #       @plottest Hyp2PB_plot_geo joinpath(references_folder, "Hyp2PBPlotGeo.png") false
 
         #        function Hyp2PB_quiver()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 0.0], [0.0, 1.0]])
         p2 = convert.(Ref(PoincareBallPoint), p)
         X = [log(M, p2[2], p2[1]), log(M, p2[1], p2[3])]
@@ -38,7 +38,7 @@ include("utils.jl")
         #        @plottest Hyp2PB_quiver joinpath(references_folder, "Hyp2PBQuiver.png") false
 
         #        function Hyp2PH_plot()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         p2 = convert.(Ref(PoincareHalfSpacePoint), p)
         #            return
@@ -47,7 +47,7 @@ include("utils.jl")
         #        @plottest Hyp2PH_plot joinpath(references_folder, "Hyp2PHPlot.png") false
 
         #        function Hyp2PH_plot_geo()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         p2 = convert.(Ref(PoincareHalfSpacePoint), p)
         #            return
@@ -56,7 +56,7 @@ include("utils.jl")
         #        @plottest Hyp2PH_plot_geo joinpath(references_folder, "Hyp2PHPlotGeo.png") false
 
         #        function Hyp2PH_quiver()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 0.0], [0.0, 1.0]])
         p2 = convert.(Ref(PoincareHalfSpacePoint), p)
         X = [log(M, p2[2], p2[1]), log(M, p2[1], p2[3])]
@@ -69,7 +69,7 @@ include("utils.jl")
         ENV["GKSwstype"] = "100"
         gr()
         #        function Hyp2_plot()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         #            return
         plot(M, p)
@@ -77,7 +77,7 @@ include("utils.jl")
         #        @plottest Hyp2_plot joinpath(references_folder, "Hyp2Plot.png") false
 
         #        function Hyp2_surfplot()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         #    return
         plot(M, p; surface=true)
@@ -85,7 +85,7 @@ include("utils.jl")
         #@plottest Hyp2_surfplot joinpath(references_folder, "Hyp2SurfPlot.png") false
 
         #        function Hyp2_plot_geo()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 1.0]])
         #            return
         plot(M, p; geodesic_interpolation=80)
@@ -93,7 +93,7 @@ include("utils.jl")
         #@plottest Hyp2_plot_geo joinpath(references_folder, "Hyp2PlotGeo.png") false
 
         #        function Hyp2_quiver()
-        M = Hyperbolic(2)
+        M = Hyperbolic(2; parameter=:type)
         p = Manifolds._hyperbolize.(Ref(M), [[1.0, 0.0], [0.0, 0.0], [0.0, 1.0]])
         X = [log(M, p[2], p[1]), log(M, p[1], p[3])]
         #           return
@@ -104,7 +104,7 @@ include("utils.jl")
     @testset "3D Recipes in pythonplot" begin
         pythonplot()
         #        function Sphere2_plot()
-        M = Sphere(2)
+        M = Sphere(2; parameter=:type)
         pts = [[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]]
         #           return
         plot(M, pts; wireframe_color=colorant"#CCCCCC", markersize=10)
@@ -112,7 +112,7 @@ include("utils.jl")
         #        @plottest Sphere2_plot joinpath(references_folder, "Sphere2Plot.png") false
 
         #        function Sphere2_surfplot()
-        M = Sphere(2)
+        M = Sphere(2; parameter=:type)
         pts = [[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]]
         #            return
         plot(M, pts; surface=true, wireframe_color=colorant"#CCCCCC", markersize=10)
@@ -120,7 +120,7 @@ include("utils.jl")
         #        @plottest Sphere2_surfplot joinpath(references_folder, "Sphere2SurfPlot.png") false
 
         #        function Sphere2_plot_geo()
-        M = Sphere(2)
+        M = Sphere(2; parameter=:type)
         pts = [[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]]
         #           return
         Plots.plot(M, pts; wireframe_color=colorant"#CCCCCC", geodesic_interpolation=80)
@@ -129,7 +129,7 @@ include("utils.jl")
 
         #        function Sphere2_quiver()
         pythonplot()
-        M = Sphere(2)
+        M = Sphere(2; parameter=:type)
         pts2 = [[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]]
         p3 = 1 / sqrt(3) .* [1.0, -1.0, 1.0]
         vecs = log.(Ref(M), pts2, Ref(p3))