diff --git a/test/unit_Hyperrectangle.jl b/test/unit_Hyperrectangle.jl
index 388f94bd02..3b4e795fe5 100644
--- a/test/unit_Hyperrectangle.jl
+++ b/test/unit_Hyperrectangle.jl
@@ -2,7 +2,7 @@ for N in [Float64, Rational{Int}, Float32]
     # random hyperrectangle
     rand(Hyperrectangle)
 
-    # center/radius/high/low
+    # center/radius/high/low/generators
     c = N[0, 0]
     r = N[1, 1]
     h = Hyperrectangle(c, r)
@@ -15,6 +15,15 @@ for N in [Float64, Rational{Int}, Float32]
         @test high(h, i) == r[i]
         @test low(h, i) == -r[i]
     end
+    gens = [Vector(g) for g in generators(h)]
+    @test ispermutation(gens, [N[1, 0], N[0, 1]])
+    @test genmat(h) ∈ [N[1 0; 0 1], N[0 1; 1 0]]
+    @test ngens(h) == 2
+    h_flat = Hyperrectangle(N[1, 2, 3, 4, 5], N[1, 0, 2, 0, 3])
+    @test collect(generators(h_flat)) ==
+        [UnitVector(1, 5, N(1)), UnitVector(3, 5, N(2)), UnitVector(5, 5, N(3))]
+    @test genmat(h_flat) == N[1 0 0; 0 0 0; 0 2 0; 0 0 0; 0 0 3]
+    @test ngens(h_flat) == 3
 
     # 1D Hyperrectangle
     h = Hyperrectangle(N[0], N[1])
diff --git a/test/unit_LineSegment.jl b/test/unit_LineSegment.jl
index 911fa2756c..0074282af5 100644
--- a/test/unit_LineSegment.jl
+++ b/test/unit_LineSegment.jl
@@ -30,8 +30,15 @@ for N in [Float64, Rational{Int}, Float32]
     @test !∈(N[7, 4], l)
     @test !∈(N[1.5, 1.6], l)
 
-    # center function
+    # center/generators
     @test center(l) == N[1.5, 1.5]
+    @test collect(generators(l)) ∈ [[N[1/2, 1/2]], [N[-1/2, -1/2]]]
+    @test genmat(l) ∈ [hcat(N[1/2 1/2]), hcat(N[-1/2, -1/2])]
+    @test ngens(l) == 1
+    l_degenerate = LineSegment(p, p)
+    @test collect(generators(l_degenerate)) == Vector{N}()
+    @test genmat(l_degenerate) == Matrix{N}(undef, 2, 0)
+    @test ngens(l_degenerate) == 0
 
     # isempty
     @test !isempty(l)
diff --git a/test/unit_Singleton.jl b/test/unit_Singleton.jl
index 470fa5ca83..46e61750e8 100644
--- a/test/unit_Singleton.jl
+++ b/test/unit_Singleton.jl
@@ -2,7 +2,7 @@ for N in [Float64, Rational{Int}, Float32]
     # random singleton
     rand(Singleton)
 
-    # center/radius/high/low
+    # center/radius/high/low/generators
     c = N[0, 0]
     r = N[0, 0]
     s = Singleton(c)
@@ -15,6 +15,9 @@ for N in [Float64, Rational{Int}, Float32]
         @test high(s, i) == r[i]
         @test low(s, i) == -r[i]
     end
+    @test collect(generators(s)) == Vector{Vector{N}}()
+    @test genmat(s) == Matrix{N}(undef, 2, 0)
+    @test ngens(s) == 0
 
     # 1D singleton
     s = Singleton(N[1])
diff --git a/test/unit_Zonotope.jl b/test/unit_Zonotope.jl
index 8b42dfc58e..d547f6db94 100644
--- a/test/unit_Zonotope.jl
+++ b/test/unit_Zonotope.jl
@@ -103,6 +103,7 @@ for N in [Float64, Rational{Int}, Float32]
     Z = Zonotope(N[2, 1], N[-0.5 1.5 0.5 1; 0.5 1.5 1 0.5])
     @test ngens(Z) == 4
     @test genmat(Z) == Z.generators
+    @test ispermutation(collect(generators(Z)), [genmat(Z)[:, j] for j in 1:ngens(Z)])
     # test order reduction
     Zred1 = reduce_order(Z, 1)
     @test ngens(Zred1) == 2
@@ -114,6 +115,10 @@ for N in [Float64, Rational{Int}, Float32]
     Zred3 = reduce_order(Z, 2)
     @test ngens(Zred3) == 4
     @test order(Zred3) == 2
+    Znogen = Zonotope(N[1, 2], Matrix{N}(undef, 2, 0))
+    @test ngens(Znogen) == 0
+    @test genmat(Znogen) == Matrix{N}(undef, 2, 0)
+    @test collect(generators(Znogen)) == Vector{N}()
 
     # test conversion from hyperrectangular sets
     Z = convert(Zonotope, Hyperrectangle(N[2, 3], N[4, 5]))