diff --git a/src/VPolygon.jl b/src/VPolygon.jl
index 33bd98a3c4..aa4cda5bdb 100644
--- a/src/VPolygon.jl
+++ b/src/VPolygon.jl
@@ -1,11 +1,9 @@
-import Base: <=, ∈
+import Base: ∈
 
-export VPolygon,
-       vertices_list,
-       singleton_list
+export VPolygon
 
 """
-    VPolygon{N<:Real} <: LazySet
+    VPolygon{N<:Real} <: AbstractPolygon{N}
 
 Type that represents a polygon by its vertices.
 
@@ -24,7 +22,7 @@ the convex hull.
             apply_convex_hull::Bool=true,
             algorithm::String="monotone_chain")`
 """
-struct VPolygon{N<:Real} <: LazySet
+struct VPolygon{N<:Real} <: AbstractPolygon{N}
     vertices_list::Vector{Vector{N}}
 
     # default constructor that applies a convex hull algorithm
@@ -39,10 +37,14 @@ struct VPolygon{N<:Real} <: LazySet
     end
 end
 
+
+# --- AbstractPolygon interface functions ---
+
+
 """
-    dim(P::VPolygon)::Int
+    tovrep(P::VPolygon{N})::VPolygon{N} where {N<:Real}
 
-Return the dimension of a polygon in vertex representation.
+Build a vertex representation of the given polygon.
 
 ### Input
 
@@ -50,53 +52,32 @@ Return the dimension of a polygon in vertex representation.
 
 ### Output
 
-The ambient dimension of the polygon.
+The identity, i.e., the same polygon instance.
 """
-function dim(P::VPolygon)::Int
-    return 2
+function tovrep(P::VPolygon{N})::VPolygon{N} where {N<:Real}
+    return P
 end
 
 """
-    σ(d::AbstractVector{<:Real}, P::VPolygon{N})::Vector{N} where {N<:Real}
+    tohrep(P::VPolygon{N})::AbstractHPolygon{N} where {N<:Real}
 
-Return the support vector of a polygon in a given direction.
+Build a constraint representation of the given polygon.
 
 ### Input
 
-- `d` -- direction
 - `P` -- polygon in vertex representation
 
 ### Output
 
-The support vector in the given direction.
-If the direction has norm zero, the first vertex is returned.
-
-### Algorithm
+The same polygon but in constraint representation, an `AbstractHPolygon`.
+"""
+function tohrep(P::VPolygon{N})::AbstractHPolygon{N} where {N<:Real}
+    error("this function is not implemented yet, see issue #5")
+end
 
-This implementation performs a brute-force search, comparing the projection of
-each vector along the given direction.
-It runs in ``O(n)`` where ``n`` is the number of vertices.
 
-### Notes
+# --- AbstractPolytope interface functions ---
 
-For arbitrary points without structure this is the best one can do.
-However, a more efficient approach can be used if the vertices of the polygon
-have been sorted in counter-clockwise fashion.
-In that case a binary search algorithm can be used that runs in ``O(\\log n)``.
-See issue [#40](https://github.com/JuliaReach/LazySets.jl/issues/40).
-"""
-function σ(d::AbstractVector{<:Real}, P::VPolygon{N})::Vector{N} where {N<:Real}
-    if isempty(P.vertices_list)
-        error("this polygon is empty")
-    end
-    i_max = 1
-    @inbounds for i in 2:length(P.vertices_list)
-        if dot(d, P.vertices_list[i] - P.vertices_list[i_max]) > zero(N)
-            i_max = i
-        end
-    end
-    return P.vertices_list[i_max]
-end
 
 """
     vertices_list(P::VPolygon{N})::Vector{Vector{N}} where {N<:Real}
@@ -115,22 +96,51 @@ function vertices_list(P::VPolygon{N})::Vector{Vector{N}} where {N<:Real}
     return P.vertices_list
 end
 
+
+# --- LazySet interface functions ---
+
+
 """
-    singleton_list(P::VPolygon{N})::Vector{Singleton{N}} where {N<:Real}
+    σ(d::AbstractVector{<:Real}, P::VPolygon{N})::Vector{N} where {N<:Real}
 
-Return the vertices of a convex polygon in vertex representation as a list of
-singletons.
+Return the support vector of a polygon in a given direction.
 
 ### Input
 
-- `P` -- a polygon vertex representation
+- `d` -- direction
+- `P` -- polygon in vertex representation
 
 ### Output
 
-List containing a singleton for each vertex.
+The support vector in the given direction.
+If the direction has norm zero, the first vertex is returned.
+
+### Algorithm
+
+This implementation performs a brute-force search, comparing the projection of
+each vector along the given direction.
+It runs in ``O(n)`` where ``n`` is the number of vertices.
+
+### Notes
+
+For arbitrary points without structure this is the best one can do.
+However, a more efficient approach can be used if the vertices of the polygon
+have been sorted in counter-clockwise fashion.
+In that case a binary search algorithm can be used that runs in ``O(\\log n)``.
+See issue [#40](https://github.com/JuliaReach/LazySets.jl/issues/40).
 """
-function singleton_list(P::VPolygon{N})::Vector{Singleton{N}} where {N<:Real}
-    return [Singleton(vi) for vi in P.vertices_list]
+function σ(d::AbstractVector{<:Real},
+           P::VPolygon{N})::Vector{N} where {N<:Real}
+    if isempty(P.vertices_list)
+        error("this polygon is empty")
+    end
+    i_max = 1
+    @inbounds for i in 2:length(P.vertices_list)
+        if dot(d, P.vertices_list[i] - P.vertices_list[i_max]) > zero(N)
+            i_max = i
+        end
+    end
+    return P.vertices_list[i_max]
 end
 
 """