diff --git a/test/topology/test_topological_invariance.jl b/test/topology/test_topological_invariance.jl
new file mode 100644
index 0000000..ad6ef73
--- /dev/null
+++ b/test/topology/test_topological_invariance.jl
@@ -0,0 +1,44 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM
+using Test
+
+@testset "Topological Invariance" begin
+    # Linear and quadratic variants have same topology
+    
+    @testset "Segments" begin
+        @test nvertices(Segment{2}()) == nvertices(Segment{3}())
+        @test nedges(Segment{2}()) == nedges(Segment{3}())
+    end
+    
+    @testset "Triangles" begin
+        @test nvertices(Triangle{3}()) == nvertices(Triangle{6}()) == nvertices(Triangle{7}()) == nvertices(Triangle{10}())
+        @test nedges(Triangle{3}()) == nedges(Triangle{6}()) == nedges(Triangle{7}()) == nedges(Triangle{10}())
+        @test nfaces(Triangle{3}()) == nfaces(Triangle{6}()) == nfaces(Triangle{7}()) == nfaces(Triangle{10}())
+    end
+    
+    @testset "Quadrilaterals" begin
+        @test nvertices(Quadrilateral{4}()) == nvertices(Quadrilateral{8}()) == nvertices(Quadrilateral{9}())
+        @test nedges(Quadrilateral{4}()) == nedges(Quadrilateral{8}()) == nedges(Quadrilateral{9}())
+        @test nfaces(Quadrilateral{4}()) == nfaces(Quadrilateral{8}()) == nfaces(Quadrilateral{9}())
+    end
+    
+    @testset "Tetrahedra" begin
+        @test nvertices(Tetrahedron{4}()) == nvertices(Tetrahedron{10}())
+        @test nedges(Tetrahedron{4}()) == nedges(Tetrahedron{10}())
+        @test nfaces(Tetrahedron{4}()) == nfaces(Tetrahedron{10}())
+    end
+    
+    @testset "Hexahedra" begin
+        @test nvertices(Hexahedron{8}()) == nvertices(Hexahedron{20}()) == nvertices(Hexahedron{27}())
+        @test nedges(Hexahedron{8}()) == nedges(Hexahedron{20}()) == nedges(Hexahedron{27}())
+        @test nfaces(Hexahedron{8}()) == nfaces(Hexahedron{20}()) == nfaces(Hexahedron{27}())
+    end
+    
+    @testset "Wedges" begin
+        @test nvertices(Wedge{6}()) == nvertices(Wedge{15}())
+        @test nedges(Wedge{6}()) == nedges(Wedge{15}())
+        @test nfaces(Wedge{6}()) == nfaces(Wedge{15}())
+    end
+end