diff --git a/src/HPolyhedron.jl b/src/HPolyhedron.jl
index 6e711a575a..91e98db08b 100644
--- a/src/HPolyhedron.jl
+++ b/src/HPolyhedron.jl
@@ -582,9 +582,9 @@ Transform a polyhedron in H-representation to a polytope in V-representation.
 
 ### Input
 
-- `P`          -- polyhedron in constraint representation
-- `backend`    -- (optional, default: `default_polyhedra_backend(P, N)`)
-                  the polyhedral computations backend
+- `P`       -- polyhedron in constraint representation
+- `backend` -- (optional, default: `default_polyhedra_backend(P, N)`) the
+               backend for polyhedral computations
 
 ### Output
 
@@ -593,8 +593,10 @@ in constraint representation.
 
 ### Notes
 
+The conversion may not preserve the numeric type (e.g., with `N == Float32`)
+depending on the backend.
 For further information on the supported backends see
-[Polyhedra's documentation](https://juliapolyhedra.github.io/Polyhedra.jl/).
+[Polyhedra's documentation](https://juliapolyhedra.github.io/Polyhedra.jl/latest/installation.html#Getting-Libraries-1).
 """
 function tovrep(P::HPoly{N};
                 backend=default_polyhedra_backend(P, N)) where {N<:Real}
diff --git a/src/HalfSpace.jl b/src/HalfSpace.jl
index 01ad3e23ac..0d4d889557 100644
--- a/src/HalfSpace.jl
+++ b/src/HalfSpace.jl
@@ -1,6 +1,7 @@
 import Base: rand,
              ∈,
-             isempty
+             isempty,
+             convert
 
 export HalfSpace, LinearConstraint,
        an_element,
@@ -31,6 +32,10 @@ struct HalfSpace{N<:Real} <: LazySet{N}
     b::N
 end
 
+function convert(::Type{HalfSpace{N}}, hs::HalfSpace) where {N<:Real}
+    return HalfSpace{N}(hs.a, hs.b)
+end
+
 """
     LinearConstraint
 
diff --git a/src/VPolytope.jl b/src/VPolytope.jl
index 2f5e295179..3b630ec0b4 100644
--- a/src/VPolytope.jl
+++ b/src/VPolytope.jl
@@ -258,16 +258,21 @@ Transform a polytope in V-representation to a polytope in H-representation.
 
 ### Input
 
-- `P`          -- polytope in vertex representation
-- `backend`    -- (optional, default: `default_polyhedra_backend(P, N)`) the polyhedral
-                  computations backend,
-                  see [Polyhedra's documentation](https://juliapolyhedra.github.io/Polyhedra.jl/latest/installation.html#Getting-Libraries-1)
-                  for further information
+- `P`       -- polytope in vertex representation
+- `backend` -- (optional, default: `default_polyhedra_backend(P, N)`) the
+               backend for polyhedral computations
 
 ### Output
 
 The `HPolytope` which is the constraint representation of the given polytope
 in vertex representation.
+
+### Notes
+
+The conversion may not preserve the numeric type (e.g., with `N == Float32`)
+depending on the backend.
+For further information on the supported backends see
+[Polyhedra's documentation](https://juliapolyhedra.github.io/Polyhedra.jl/latest/installation.html#Getting-Libraries-1).
 """
 function tohrep(P::VPolytope{N};
                 backend=default_polyhedra_backend(P, N)) where {N<:Real}
diff --git a/test/unit_HalfSpace.jl b/test/unit_HalfSpace.jl
index 71b74cc3d4..7f3eeb0abe 100644
--- a/test/unit_HalfSpace.jl
+++ b/test/unit_HalfSpace.jl
@@ -6,6 +6,11 @@ for N in [Float64, Rational{Int}, Float32]
     normal = ones(N, 3)
     hs = HalfSpace(normal, N(5))
 
+    # numeric-type conversion preserves vector base type
+    hs1 = HalfSpace(spzeros(4), 1.)
+    hs2 = convert(HalfSpace{N}, hs1)
+    @test hs2.a isa SparseVector{N}
+
     # dimension
     @test dim(hs) == 3
 
diff --git a/test/unit_Polytope.jl b/test/unit_Polytope.jl
index 79e1edafc8..25debd5499 100644
--- a/test/unit_Polytope.jl
+++ b/test/unit_Polytope.jl
@@ -135,6 +135,31 @@ end
 @test HPolytope() isa HPolytope{Float64}
 @test VPolytope() isa VPolytope{Float64}
 
+# Polyhedra tests that do not work with Float32
+if test_suite_polyhedra
+    for N in [Float64, Rational{Int}]
+        # CDDLib does not preserve the Rational{Int} type
+        if VERSION >= v"0.7" || N == Float64
+            # tovrep from HPolytope
+            A = N[0 1; 1 0; -1 -1]
+            b = N[0.25, 0.25, -0]
+            P = HPolytope(A, b)
+            @test tovrep(P) isa VPolytope{N}
+            @test tohrep(P) isa HPolytope{N}  # no-op
+
+            # tohrep from VPolytope
+            v1 = N[1, 0]
+            v2 = N[0, 1]
+            v3 = N[-1, 0]
+            v4 = N[0, -1]
+            v5 = N[0, 0]
+            P = VPolytope([v1, v2, v3, v4, v5])
+            @test tohrep(P) isa HPolytope{N}
+            @test tovrep(P) isa VPolytope{N}  # no-op
+        end
+    end
+end
+
 # Polyhedra tests that only work with Float64
 if test_suite_polyhedra
     for N in [Float64]
@@ -186,13 +211,6 @@ if test_suite_polyhedra
         vl = vertices_list(p)
         @test ispermutation(vl, [N[0], N[1]])
 
-        # 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
-
         # checking for emptiness
         P = HPolytope([LinearConstraint(N[1, 0], N(0))])    # x <= 0
         @test !isempty(P)
@@ -243,10 +261,5 @@ if test_suite_polyhedra
         cp = cartesian_product(p1, p2)
         vl = vertices_list(cp)
         @test ispermutation(vl, [N[0, 0, 2], N[1, 1, 2]])
-
-        # tohrep from VPolytope
-        P = VPolytope([v1, v2, v3, v4, v5])
-        @test tohrep(P) isa HPolytope
-        @test tovrep(P) isa VPolytope # no-op
     end
 end