diff --git a/src/LinearMap.jl b/src/LinearMap.jl
index 82bcb4e0f7..32d0eba809 100644
--- a/src/LinearMap.jl
+++ b/src/LinearMap.jl
@@ -316,13 +316,14 @@ function isempty(lm::LinearMap)::Bool
 end
 
 """
-    vertices_list(lm::LinearMap{N})::Vector{Vector{N}} where {N<:Real}
+    vertices_list(lm::LinearMap{N}; prune::Bool=true)::Vector{Vector{N}} where {N<:Real}
 
 Return the list of vertices of a (polyhedral) linear map.
 
 ### Input
 
 - `lm` -- linear map
+- `prune` -- (optional, default: `true`) if true removes redundant vertices
 
 ### Output
 
@@ -333,7 +334,7 @@ A list of vertices.
 We assume that the underlying set `X` is polyhedral.
 Then the result is just the linear map applied to the vertices of `X`.
 """
-function vertices_list(lm::LinearMap{N})::Vector{Vector{N}} where {N<:Real}
+function vertices_list(lm::LinearMap{N}; prune::Bool=true)::Vector{Vector{N}} where {N<:Real}
     # for a zero map, the result is just the list containing the origin
     if iszero(lm.M)
         return [zeros(N, dim(lm))]
@@ -349,7 +350,7 @@ function vertices_list(lm::LinearMap{N})::Vector{Vector{N}} where {N<:Real}
         push!(vlist, lm.M * v)
     end
 
-    return vlist
+    return prune ? convex_hull(vlist) : vlist
 end
 
 """
diff --git a/test/unit_LinearMap.jl b/test/unit_LinearMap.jl
index 9b49dcb501..026785998a 100644
--- a/test/unit_LinearMap.jl
+++ b/test/unit_LinearMap.jl
@@ -84,6 +84,11 @@ for N in [Float64, Rational{Int}, Float32]
     vlist = vertices_list(LinearMap(M, b))
     @test vlist == [zeros(N, 2)]
 
+    # test that redundant vertices are removed by default (see #1355)
+    X = Interval(N(0), N(1)) × ZeroSet{N}(1)
+    M = N[0 1; 0 2]
+    @test vertices_list(M * X) == [N[0, 0]]
+
     if test_suite_polyhedra
         # constraints_list
         b = BallInf(N[0, 0], N(1))