diff --git a/src/HPolytope.jl b/src/HPolytope.jl
index 72efdd8538..d1a4f68fc1 100644
--- a/src/HPolytope.jl
+++ b/src/HPolytope.jl
@@ -213,7 +213,7 @@ import Polyhedra:polyhedron, SimpleHRepresentation, SimpleHRepresentation,
                  hcartesianproduct,
                  points
 
-export intersection, convex_hull, cartesian_product, vertices_list
+export intersection, convex_hull, cartesian_product, vertices_list, tovrep, tohrep
 
 # HPolytope from an HRep
 function HPolytope(P::HRep{N, T}, backend=CDDLib.CDDLibrary()) where {N, T}
@@ -370,5 +370,47 @@ function vertices_list(P::HPolytope{N};
     prunefunc(P)
     return collect(points(P))
 end
+
+"""
+    tovrep(P::HPolytope; backend=CDDLib.CDDLibrary())
+
+Transform a polytope in H-representation to a polytope in V-representation.
+
+### Input
+
+- `P`          -- polytope in constraint representation
+- `backend`    -- (optional, default: `CDDLib.CDDLibrary()`) the polyhedral
+                  computations backend,
+                  see [Polyhedra's documentation](https://juliapolyhedra.github.io/Polyhedra.jl/latest/installation.html#Getting-Libraries-1)
+                  for further information
+
+### Output
+
+The `VPolytope` which is the vertex representation of the given polytope
+in constraint representation.
+"""
+function tovrep(P::HPolytope; backend=CDDLib.CDDLibrary())
+    P = polyhedron(P, backend)
+    return VPolytope(P)
+end
+
+"""
+    tohrep(P::HPolytope)
+
+Return a constraint representation of the given polytope in constraint
+representation (no-op).
+
+### Input
+
+- `P` -- polytope in constraint representation
+
+### Output
+
+The same polytope instance.
+"""
+function tohrep(P::HPolytope)
+    return P
+end
+
 end # quote
 end # function load_polyhedra_hpolytope()
diff --git a/src/VPolytope.jl b/src/VPolytope.jl
index f8b51d5680..aee02c8405 100644
--- a/src/VPolytope.jl
+++ b/src/VPolytope.jl
@@ -129,7 +129,7 @@ import Polyhedra:polyhedron, SimpleHRepresentation, SimpleVRepresentation,
                  convexhull,
                  hcartesianproduct
 
-export intersection, convex_hull, cartesian_product, vertices_list
+export intersection, convex_hull, cartesian_product, vertices_list, tohrep, tovrep
 
 # VPolytope from a VRep
 function VPolytope(P::VRep{N, T}, backend=CDDLib.CDDLibrary()) where {N, T}
@@ -237,5 +237,46 @@ function cartesian_product(P1::VPolytope, P2::VPolytope; backend=CDDLib.CDDLibra
     return VPolytope(Pcp)
 end
 
+"""
+    tohrep(P::VPolytope; backend=CDDLib.CDDLibrary())
+
+Transform a polytope in V-representation to a polytope in H-representation.
+
+### Input
+
+- `P`          -- polytope in vertex representation
+- `backend`    -- (optional, default: `CDDLib.CDDLibrary()`) the polyhedral
+                  computations backend,
+                  see [Polyhedra's documentation](https://juliapolyhedra.github.io/Polyhedra.jl/latest/installation.html#Getting-Libraries-1)
+                  for further information
+
+### Output
+
+The `HPolytope` which is the constraint representation of the given polytope
+in vertex representation.
+"""
+function tohrep(P::VPolytope; backend=CDDLib.CDDLibrary())
+    P = polyhedron(P, backend)
+    return HPolytope(P)
+end
+
+"""
+    tovrep(P::VPolytope)
+
+Return a vertex representation of the given polytope in vertex
+representation (no-op).
+
+### Input
+
+- `P` -- polytope in vertex representation
+
+### Output
+
+The same polytope instance.
+"""
+function tovrep(P::VPolytope)
+    return P
+end
+
 end # quote
 end # function load_polyhedra_vpolytope()
diff --git a/test/unit_Polytope.jl b/test/unit_Polytope.jl
index d86bb42a88..de6fc5e543 100644
--- a/test/unit_Polytope.jl
+++ b/test/unit_Polytope.jl
@@ -72,7 +72,7 @@ for N in [Float64, Rational{Int}, Float32]
     d = N[1, 0]
     @test_throws ErrorException σ(d, p, algorithm="xyz")
     if test_suite_polyhedra
-        @test_throws MethodError σ(d, p) # not implemented yet
+        @test σ(d, p) == N[1.0, 0.0]
     else
         @test_throws AssertionError σ(d, p)
     end
@@ -128,6 +128,13 @@ if test_suite_polyhedra
         vl = vertices_list(p)
         @test length(vl) == 2 && N[0] ∈ vl && [1] ∈ vl
 
+        # tovrep from HPolytope
+        A = [N(0) N(-1); N(-1) N(0); N(1) N(1)]
+        b = N[-0.25, -0.25, -0]
+        P = HPolytope(A, b)
+        @test tovrep(P) isa VPolytope
+        @test tohrep(P) isa HPolytope # test no-op
+
         # -----
         # V-rep
         # -----
@@ -160,5 +167,10 @@ if test_suite_polyhedra
         cp = cartesian_product(p1, p2)
         vl = vertices_list(cp)
         @test length(vl) == 2 && N[0, 0, 2] ∈ vl && N[1, 1, 2] ∈ vl
+
+        # tohrep from VPolytope
+        P = VPolytope([v1, v2, v3, v4, v5])
+        @test tohrep(P) isa HPolytope
+        @test tovrep(P) isa VPolytope # no-op
     end
 end