diff --git a/docs/src/lib/sets/EmptySet.md b/docs/src/lib/sets/EmptySet.md
index 92c784e062..31f6a9246f 100644
--- a/docs/src/lib/sets/EmptySet.md
+++ b/docs/src/lib/sets/EmptySet.md
@@ -12,32 +12,9 @@ EmptySet
 ## Operations
 
 ```@docs
-an_element(::EmptySet)
-area(::EmptySet)
 chebyshev_center_radius(::EmptySet; kwargs...)
 complement(::EmptySet{N}) where {N}
-diameter(::EmptySet, ::Real=Inf)
-dim(::EmptySet)
-high(::EmptySet)
-high(::EmptySet, ::Int)
-isbounded(::EmptySet)
-isempty(::EmptySet)
-isuniversal(::EmptySet{N}, ::Bool=false) where {N}
-low(::EmptySet)
-low(::EmptySet, ::Int)
-norm(::EmptySet, ::Real=Inf)
-radius(::EmptySet, ::Real=Inf)
 rand(::Type{EmptySet})
-rectify(::EmptySet)
-reflect(::EmptySet)
-vertices_list(::EmptySet)
-vertices(::EmptySet)
-volume(::EmptySet{N}) where {N}
-∈(::AbstractVector, ::EmptySet)
-linear_map(::AbstractMatrix, ::EmptySet)
-ρ(::AbstractVector, ::EmptySet)
-σ(::AbstractVector, ::EmptySet)
-translate(::EmptySet, ::AbstractVector)
 plot_recipe(::EmptySet{N}, ::Any=zero(N)) where {N}
 ```
 
@@ -46,15 +23,36 @@ CurrentModule = LazySets.API
 ```
 
 Undocumented implementations:
+
+* [`an_element`](@ref an_element(::LazySet))
+* [`area`](@ref area(::LazySet))
 * [`convex_hull`](@ref convex_hull(::LazySet))
+* [`diameter`](@ref diameter(::LazySet, ::Real=Inf))
+* [`dim`](@ref dim(::LazySet))
+* [`high`](@ref high(::LazySet))
+* [`high`](@ref high(::LazySet, ::Int))
+* [`isbounded`](@ref isbounded(::LazySet))
 * [`isboundedtype`](@ref isboundedtype(::Type{LazySet}))
 * [`isconvextype`](@ref isconvextype(::Type{LazySet}))
+* [`isempty`](@ref isempty(::LazySet))
 * [`isoperationtype`](@ref isoperationtype(::Type{LazySet}))
-* [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
-* [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
+* [`isuniversal`](@ref isuniversal(::LazySet, ::Bool=false))
+* [`low`](@ref low(::LazySet))
+* [`low`](@ref low(::LazySet, ::Int))
+* [`norm`](@ref norm(::LazySet, ::Real=Inf))
+* [`radius`](@ref radius(::LazySet, ::Real=Inf))
+* [`rectify`](@ref rectify(::LazySet))
+* [`reflect`](@ref reflect(::LazySet))
+* [`vertices_list`](@ref vertices_list(::LazySet))
+* [`vertices`](@ref vertices(::LazySet))
+* [`volume`](@ref volume(::LazySet))
+* [`∈`](@ref ∈(::AbstractVector, ::LazySet))
+* [`linear_map`](@ref linear_map(::AbstractMatrix, ::LazySet))
+* [`ρ`](@ref ρ(::AbstractVector, ::LazySet))
+* [`σ`](@ref σ(::AbstractVector, ::LazySet))
 * [`scale`](@ref scale(::Real, ::LazySet))
 * [`scale!`](@ref scale!(::Real, ::LazySet))
+* [`translate`](@ref translate(::LazySet, ::AbstractVector))
 * [`translate!`](@ref translate!(::LazySet, ::AbstractVector))
 * [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`intersection`](@ref isequivalent(::LazySet, ::LazySet))
@@ -75,6 +73,9 @@ Inherited from [`LazySet`](@ref):
 * [`ispolyhedral`](@ref ispolyhedral(::LazySet))
 * [`singleton_list`](@ref singleton_list(::LazySet))
 * [`surface`](@ref surface(::LazySet))
+* [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
+* [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`cartesian_product`](@ref cartesian_product(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`==`](@ref ==(::LazySet, ::LazySet))
diff --git a/src/Sets/EmptySet/an_element.jl b/src/Sets/EmptySet/an_element.jl
index b6b84b1602..a2094b587e 100644
--- a/src/Sets/EmptySet/an_element.jl
+++ b/src/Sets/EmptySet/an_element.jl
@@ -1,16 +1,3 @@
-"""
-    an_element(∅::EmptySet)
-
-Return some element of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-An error.
-"""
 function an_element(::EmptySet)
-    return error("an empty set does not contain any element")
+    throw(ArgumentError("an empty set does not contain any element"))
 end
diff --git a/src/Sets/EmptySet/area.jl b/src/Sets/EmptySet/area.jl
index ff33f3d676..e9e89399d5 100644
--- a/src/Sets/EmptySet/area.jl
+++ b/src/Sets/EmptySet/area.jl
@@ -1,16 +1,3 @@
-"""
-    area(∅::EmptySet)
-
-Return the area of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-``0``.
-"""
 function area(∅::EmptySet)
     N = eltype(∅)
     return zero(N)
diff --git a/src/Sets/EmptySet/chebyshev_center_radius.jl b/src/Sets/EmptySet/chebyshev_center_radius.jl
index d68a4a97b4..2682f57a1e 100644
--- a/src/Sets/EmptySet/chebyshev_center_radius.jl
+++ b/src/Sets/EmptySet/chebyshev_center_radius.jl
@@ -14,5 +14,5 @@ and the corresponding radius of an empty set.
 An error.
 """
 function chebyshev_center_radius(∅::EmptySet; kwargs...)
-    return error("the Chebyshev center and radius of an empty set are undefined")
+    throw(ArgumentError("the Chebyshev center and radius of an empty set are undefined"))
 end
diff --git a/src/Sets/EmptySet/complement.jl b/src/Sets/EmptySet/complement.jl
index 321f3ce1b7..73eff228fb 100644
--- a/src/Sets/EmptySet/complement.jl
+++ b/src/Sets/EmptySet/complement.jl
@@ -1,15 +1,11 @@
 """
-    complement(∅::EmptySet{N}) where {N}
-
-Return the complement of an empty set.
+# Extended help
 
-### Input
-
-- `∅` -- empty set
+    complement(∅::EmptySet{N}) where {N}
 
 ### Output
 
-The universe of the same dimension.
+The [`Universe`](@ref) of the same dimension.
 """
 function complement(∅::EmptySet{N}) where {N}
     require(@__MODULE__, :LazySets; fun_name="complement")
diff --git a/src/Sets/EmptySet/convex_hull.jl b/src/Sets/EmptySet/convex_hull.jl
index f3e34187d5..c1a986e5d8 100644
--- a/src/Sets/EmptySet/convex_hull.jl
+++ b/src/Sets/EmptySet/convex_hull.jl
@@ -1 +1,9 @@
-convex_hull(∅::EmptySet, ::EmptySet) = ∅
+function convex_hull(∅::EmptySet)
+    return ∅
+end
+
+function convex_hull(∅₁::EmptySet, ∅₂::EmptySet)
+    @assert dim(∅₁) == dim(∅₂) "cannot take the convex hull between two " *
+                               "empty sets of dimensions $(dim(∅₁)) and $(dim(∅₂))"
+    return ∅₁
+end
diff --git a/src/Sets/EmptySet/diameter.jl b/src/Sets/EmptySet/diameter.jl
index 772eae8d1c..1e57ef52bd 100644
--- a/src/Sets/EmptySet/diameter.jl
+++ b/src/Sets/EmptySet/diameter.jl
@@ -1,20 +1,3 @@
-"""
-    diameter(∅::EmptySet, [p]::Real=Inf)
-
-Return the diameter of an empty set.
-It is the maximum distance between any two elements of the set or, equivalently,
-the diameter of the enclosing ball (of the given ``p``-norm) of minimal volume
-with the same center.
-
-### Input
-
-- `∅` -- empty set
-- `p` -- (optional, default: `Inf`) norm
-
-### Output
-
-An error.
-"""
 function diameter(::EmptySet, ::Real=Inf)
-    return error("the diameter of an empty set is undefined")
+    throw(ArgumentError("the diameter of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/dim.jl b/src/Sets/EmptySet/dim.jl
index 900e6b19d4..5d404009ff 100644
--- a/src/Sets/EmptySet/dim.jl
+++ b/src/Sets/EmptySet/dim.jl
@@ -1,16 +1,3 @@
-"""
-    dim(∅::EmptySet)
-
-Return the dimension of an empty set.
-
-### Input
-
-- `∅` -- an empty set
-
-### Output
-
-The dimension of the empty set.
-"""
 function dim(∅::EmptySet)
     return ∅.dim
 end
diff --git a/src/Sets/EmptySet/high.jl b/src/Sets/EmptySet/high.jl
index 3032a53f40..a85e8ac7a4 100644
--- a/src/Sets/EmptySet/high.jl
+++ b/src/Sets/EmptySet/high.jl
@@ -1,39 +1,7 @@
-"""
-    high(∅::EmptySet)
-
-Return a vector with the highest coordinates of an empty set in each canonical
-direction.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-An error.
-
-### Notes
-
-See also [`high(∅::EmptySet, i::Int)`](@ref).
-"""
 function high(::EmptySet)
-    return error("the upper bound of an empty set is undefined")
+    throw(ArgumentError("the upper bound of an empty set is undefined"))
 end
 
-"""
-    high(∅::EmptySet, i::Int)
-
-Return the highest coordinate of an empty set in the given direction.
-
-### Input
-
-- `∅` -- empty set
-- `i` -- dimension of interest
-
-### Output
-
-An error.
-"""
 function high(::EmptySet, ::Int)
-    return error("the upper bound of an empty set is undefined")
+    throw(ArgumentError("the upper bound of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/in.jl b/src/Sets/EmptySet/in.jl
index ffa7918bc8..63ef72d48c 100644
--- a/src/Sets/EmptySet/in.jl
+++ b/src/Sets/EmptySet/in.jl
@@ -1,24 +1,3 @@
-"""
-    ∈(x::AbstractVector, ∅::EmptySet)
-
-Check whether a given point is contained in an empty set.
-
-### Input
-
-- `x` -- point/vector
-- `∅` -- empty set
-
-### Output
-
-`false`.
-
-### Examples
-
-```jldoctest
-julia> [1.0, 0.0] ∈ ∅(2)
-false
-```
-"""
 function ∈(::AbstractVector, ::EmptySet)
     return false
 end
diff --git a/src/Sets/EmptySet/isbounded.jl b/src/Sets/EmptySet/isbounded.jl
index d39b35237d..6e3cacd2f4 100644
--- a/src/Sets/EmptySet/isbounded.jl
+++ b/src/Sets/EmptySet/isbounded.jl
@@ -1,16 +1,3 @@
-"""
-    isbounded(∅::EmptySet)
-
-Check whether an empty set is bounded.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-`true`.
-"""
 function isbounded(::EmptySet)
     return true
 end
diff --git a/src/Sets/EmptySet/isempty.jl b/src/Sets/EmptySet/isempty.jl
index 15510cf918..3c3c29cce8 100644
--- a/src/Sets/EmptySet/isempty.jl
+++ b/src/Sets/EmptySet/isempty.jl
@@ -1,16 +1,3 @@
-"""
-    isempty(∅::EmptySet)
-
-Check if the empty set is empty.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-`true`.
-"""
 function isempty(::EmptySet)
     return true
 end
diff --git a/src/Sets/EmptySet/isuniversal.jl b/src/Sets/EmptySet/isuniversal.jl
index d6536da26f..22544ed02b 100644
--- a/src/Sets/EmptySet/isuniversal.jl
+++ b/src/Sets/EmptySet/isuniversal.jl
@@ -1,18 +1,3 @@
-"""
-    isuniversal(∅::EmptySet{N}, [witness]::Bool=false) where {N}
-
-Check whether an empty set is universal.
-
-### Input
-
-- `∅`       -- empty set
-- `witness` -- (optional, default: `false`) compute a witness if activated
-
-### Output
-
-* If `witness` option is deactivated: `false`
-* If `witness` option is activated: `(false, v)` where ``v ∉ S``
-"""
 function isuniversal(∅::EmptySet{N}, witness::Bool=false) where {N}
     if witness
         return (false, zeros(N, dim(∅)))
diff --git a/src/Sets/EmptySet/linear_map.jl b/src/Sets/EmptySet/linear_map.jl
index 83d1395e77..3980b2cc19 100644
--- a/src/Sets/EmptySet/linear_map.jl
+++ b/src/Sets/EmptySet/linear_map.jl
@@ -1,21 +1,7 @@
-"""
-    linear_map(M::AbstractMatrix{N}, ∅::EmptySet{N}) where {N}
-
-Return the linear map of an empty set.
-
-### Input
-
-- `M` -- matrix
-- `∅` -- empty set
-
-### Output
-
-An empty set.
-"""
 function linear_map(M::AbstractMatrix, ∅::EmptySet)
-    N = eltype(∅)
     @assert size(M, 2) == dim(∅) "cannot apply a $(size(M))-dimensional " *
                                  "matrix to a $(dim(∅))-dimensional set"
 
+    N = eltype(∅)
     return EmptySet{N}(size(M, 1))
 end
diff --git a/src/Sets/EmptySet/low.jl b/src/Sets/EmptySet/low.jl
index 5ea5a5cbeb..1d4a59c745 100644
--- a/src/Sets/EmptySet/low.jl
+++ b/src/Sets/EmptySet/low.jl
@@ -1,39 +1,7 @@
-"""
-    low(∅::EmptySet)
-
-Return a vector with the lowest coordinates of an empty set in each canonical
-direction.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-An error.
-
-### Notes
-
-See also [`low(∅::EmptySet, i::Int)`](@ref).
-"""
 function low(::EmptySet)
-    return error("the lower bound of an empty set is undefined")
+    throw(ArgumentError("the lower bound of an empty set is undefined"))
 end
 
-"""
-    low(∅::EmptySet, i::Int)
-
-Return the lowest coordinate of an empty set in the given direction.
-
-### Input
-
-- `∅` -- empty set
-- `i` -- dimension of interest
-
-### Output
-
-An error.
-"""
 function low(::EmptySet, ::Int)
-    return error("the lower bound of an empty set is undefined")
+    throw(ArgumentError("the lower bound of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/norm.jl b/src/Sets/EmptySet/norm.jl
index d28534c461..53765124de 100644
--- a/src/Sets/EmptySet/norm.jl
+++ b/src/Sets/EmptySet/norm.jl
@@ -1,19 +1,3 @@
-"""
-    norm(∅::EmptySet, [p]::Real=Inf)
-
-Return the norm of an empty set.
-It is the norm of the enclosing ball (of the given ``p``-norm) of minimal volume
-that is centered in the origin.
-
-### Input
-
-- `∅` -- empty set
-- `p` -- (optional, default: `Inf`) norm
-
-### Output
-
-An error.
-"""
 function norm(::EmptySet, ::Real=Inf)
-    return error("the norm of an empty set is undefined")
+    throw(ArgumentError("the norm of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/radius.jl b/src/Sets/EmptySet/radius.jl
index 1fa7684402..6727e5e370 100644
--- a/src/Sets/EmptySet/radius.jl
+++ b/src/Sets/EmptySet/radius.jl
@@ -1,19 +1,3 @@
-"""
-    radius(∅::EmptySet, [p]::Real=Inf)
-
-Return the radius of an empty set.
-It is the radius of the enclosing ball (of the given ``p``-norm) of minimal
-volume with the same center.
-
-### Input
-
-- `∅` -- empty set
-- `p` -- (optional, default: `Inf`) norm
-
-### Output
-
-An error.
-"""
 function radius(::EmptySet, ::Real=Inf)
-    return error("the radius of an empty set is undefined")
+    throw(ArgumentError("the radius of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/rand.jl b/src/Sets/EmptySet/rand.jl
index d66012e270..d02b67224e 100644
--- a/src/Sets/EmptySet/rand.jl
+++ b/src/Sets/EmptySet/rand.jl
@@ -1,20 +1,12 @@
 """
+# Extended help
+
     rand(::Type{EmptySet}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
          [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing)
 
-Create an empty set (note that there is nothing to randomize).
-
-### Input
-
-- `EmptySet` -- type for dispatch
-- `N`        -- (optional, default: `Float64`) numeric type
-- `dim`      -- (optional, default: 2) dimension
-- `rng`      -- (optional, default: `GLOBAL_RNG`) random number generator
-- `seed`     -- (optional, default: `nothing`) seed for reseeding
-
 ### Output
 
-The (only) empty set of the given numeric type and dimension.
+The (unique) empty set of the given numeric type and dimension.
 """
 function rand(::Type{EmptySet};
               N::Type{<:Real}=Float64,
diff --git a/src/Sets/EmptySet/rectify.jl b/src/Sets/EmptySet/rectify.jl
index 08482a7e20..ac6783aaad 100644
--- a/src/Sets/EmptySet/rectify.jl
+++ b/src/Sets/EmptySet/rectify.jl
@@ -1,16 +1,3 @@
-"""
-    rectify(∅::EmptySet)
-
-Concrete rectification of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-The empty set.
-"""
 function rectify(∅::EmptySet)
     return ∅
 end
diff --git a/src/Sets/EmptySet/reflect.jl b/src/Sets/EmptySet/reflect.jl
index 48fff31488..e5e5108a2b 100644
--- a/src/Sets/EmptySet/reflect.jl
+++ b/src/Sets/EmptySet/reflect.jl
@@ -1,16 +1,3 @@
-"""
-    reflect(∅::EmptySet)
-
-Concrete reflection of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-The same empty set.
-"""
 function reflect(∅::EmptySet)
     return ∅
 end
diff --git a/src/Sets/EmptySet/support_function.jl b/src/Sets/EmptySet/support_function.jl
index 3f201c81a3..4ec4bab7cb 100644
--- a/src/Sets/EmptySet/support_function.jl
+++ b/src/Sets/EmptySet/support_function.jl
@@ -1,17 +1,3 @@
-"""
-    ρ(d::AbstractVector, ∅::EmptySet)
-
-Evaluate the support function of an empty set in a given direction.
-
-### Input
-
-- `d` -- direction
-- `∅` -- empty set
-
-### Output
-
-An error.
-"""
 function ρ(::AbstractVector, ::EmptySet)
-    return error("the support function of an empty set is undefined")
+    throw(ArgumentError("the support function of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/support_vector.jl b/src/Sets/EmptySet/support_vector.jl
index 0f6c8d16d7..cf7542b9c2 100644
--- a/src/Sets/EmptySet/support_vector.jl
+++ b/src/Sets/EmptySet/support_vector.jl
@@ -1,17 +1,3 @@
-"""
-    σ(d::AbstractVector, ∅::EmptySet)
-
-Return the support vector of an empty set.
-
-### Input
-
-- `d` -- direction
-- `∅` -- empty set
-
-### Output
-
-An error.
-"""
 function σ(::AbstractVector, ::EmptySet)
-    return error("the support vector of an empty set is undefined")
+    throw(ArgumentError("the support vector of an empty set is undefined"))
 end
diff --git a/src/Sets/EmptySet/translate.jl b/src/Sets/EmptySet/translate.jl
index eda2777b77..d2cbc8a39a 100644
--- a/src/Sets/EmptySet/translate.jl
+++ b/src/Sets/EmptySet/translate.jl
@@ -1,17 +1,3 @@
-"""
-    translate(∅::EmptySet, v::AbstractVector)
-
-Translate (i.e., shift) an empty set by a given vector.
-
-### Input
-
-- `∅` -- empty set
-- `v` -- translation vector
-
-### Output
-
-The empty set.
-"""
 function translate(∅::EmptySet, v::AbstractVector)
     return translate!(∅, v)  # no need to copy
 end
diff --git a/src/Sets/EmptySet/vertices.jl b/src/Sets/EmptySet/vertices.jl
index d8b214ca02..11866e918a 100644
--- a/src/Sets/EmptySet/vertices.jl
+++ b/src/Sets/EmptySet/vertices.jl
@@ -1,16 +1,3 @@
-"""
-    vertices(∅::EmptySet)
-
-Construct an iterator over the vertices of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-The empty iterator, as the empty set does not contain any vertices.
-"""
 function vertices(∅::EmptySet)
     N = eltype(∅)
     return EmptyIterator{Vector{N}}()
diff --git a/src/Sets/EmptySet/vertices_list.jl b/src/Sets/EmptySet/vertices_list.jl
index dffbf08197..e2d15c7b40 100644
--- a/src/Sets/EmptySet/vertices_list.jl
+++ b/src/Sets/EmptySet/vertices_list.jl
@@ -1,16 +1,3 @@
-"""
-    vertices_list(∅::EmptySet)
-
-Return the list of vertices of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-The empty list of vertices, as the empty set does not contain any vertices.
-"""
 function vertices_list(∅::EmptySet)
     N = eltype(∅)
     return Vector{Vector{N}}()
diff --git a/src/Sets/EmptySet/volume.jl b/src/Sets/EmptySet/volume.jl
index aba8129fe1..3b27bdce06 100644
--- a/src/Sets/EmptySet/volume.jl
+++ b/src/Sets/EmptySet/volume.jl
@@ -1,16 +1,3 @@
-"""
-    volume(∅::EmptySet{N}) where {N}
-
-Return the volume of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-``0``.
-"""
 function volume(::EmptySet{N}) where {N}
     return zero(N)
 end
diff --git a/test/Sets/EmptySet.jl b/test/Sets/EmptySet.jl
index 41f6ae7d07..0892a36a25 100644
--- a/test/Sets/EmptySet.jl
+++ b/test/Sets/EmptySet.jl
@@ -9,8 +9,8 @@ for N in [Float64, Rational{Int}, Float32]
     @test dim(E) == 2
 
     # support function & support vector
-    @test_throws ErrorException ρ(N[0], E)
-    @test_throws ErrorException σ(N[0], E)
+    @test_throws ArgumentError ρ(N[0], E)
+    @test_throws ArgumentError σ(N[0], E)
 
     # boundedness
     @test isbounded(E) && isboundedtype(typeof(E))
@@ -36,10 +36,10 @@ for N in [Float64, Rational{Int}, Float32]
     @test isempty(E)
 
     # an_element/norm/radius/diameter functions
-    @test_throws ErrorException an_element(E)
-    @test_throws ErrorException norm(E)
-    @test_throws ErrorException radius(E)
-    @test_throws ErrorException diameter(E)
+    @test_throws ArgumentError an_element(E)
+    @test_throws ArgumentError norm(E)
+    @test_throws ArgumentError radius(E)
+    @test_throws ArgumentError diameter(E)
 
     # vertices / vertices_list
     @test collect(vertices(E)) == vertices_list(E) == Vector{Vector{N}}()
@@ -84,13 +84,13 @@ for N in [Float64, Rational{Int}, Float32]
     @test area(E) == N(0)
 
     # chebyshev_center_radius
-    @test_throws ErrorException chebyshev_center_radius(E)
+    @test_throws ArgumentError chebyshev_center_radius(E)
 
     # low/high
-    @test_throws ErrorException low(E)
-    @test_throws ErrorException low(E, 1)
-    @test_throws ErrorException high(E)
-    @test_throws ErrorException high(E, 1)
+    @test_throws ArgumentError low(E)
+    @test_throws ArgumentError low(E, 1)
+    @test_throws ArgumentError high(E)
+    @test_throws ArgumentError high(E, 1)
 
     # isdisjoint
     @test isdisjoint(E, B) && isdisjoint(B, E) && isdisjoint(E, E)