diff --git a/src/Approximations/decompositions.jl b/src/Approximations/decompositions.jl
index fa1e9d5ac1..ed2f62df3e 100644
--- a/src/Approximations/decompositions.jl
+++ b/src/Approximations/decompositions.jl
@@ -659,3 +659,11 @@ function project(H::AbstractHyperrectangle, block::AbstractVector{Int})
     πr = radius_hyperrectangle(H)[block]
     return Hyperrectangle(πc, πr, check_bounds=false)
 end
+
+function project(V::Union{<:VPolygon{N}, <:VPolytope{N}},
+                 block::AbstractVector{Int}) where {N}
+    n = dim(V)
+    M = projection_matrix(block, n, N)
+    πvertices = broadcast(v -> M * v, vertices_list(V))
+    return VPolytope(πvertices)
+end
diff --git a/test/unit_Polygon.jl b/test/unit_Polygon.jl
index 9738290859..27968f9201 100644
--- a/test/unit_Polygon.jl
+++ b/test/unit_Polygon.jl
@@ -391,6 +391,12 @@ for N in [Float64, Float32, Rational{Int}]
     m = N[4 0; 6 2; 4 4]'
     P = VPolygon(m)
     @test is_cyclic_permutation(vertices_list(P), [N[4, 0], N[6, 2], N[4, 4]])
+
+    # test concrete projection
+    V = VPolygon([N[0, 1], N[1, 0], N[-1, 0]])
+    @test project(V, [1]) == VPolytope([N[-1], N[1], N[0]])
+    V = VPolygon([N[1, 0], N[1, 1]])
+    @test project(V, [1]) == VPolytope([N[1], N[1]])
 end
 
 function same_constraints(v::Vector{<:LinearConstraint{N}})::Bool where N<:Real
diff --git a/test/unit_Polytope.jl b/test/unit_Polytope.jl
index bcab23e655..8bfb0fd3be 100644
--- a/test/unit_Polytope.jl
+++ b/test/unit_Polytope.jl
@@ -194,6 +194,11 @@ for N in [Float64, Rational{Int}, Float32]
     p[1] = N(5)
     # test that Pcopy is independent of P ( = deepcopy)
     @test Pcopy.vertices[1] == [N(1)]
+
+    # test concrete projection
+    V = VPolytope([N[0, 0, 1], N[0, 1, 0], N[0, -1, 0], N[1, 0, 0]])
+    @test project(V, [1]) == VPolytope([N[0], N[0], N[0], N[1]])
+    @test project(V, [1, 2]) == VPolytope([N[0, 0], N[0, 1], N[0, -1], N[1, 0]])
 end
 
 # default Float64 constructors