Algebraic Construction of a Klein Bottle

\(klein\  = \ 
      \(GroebnerBasis[
          {\((2 + c\_u\ s\_t - 2  c\_t\ s\_t\ s\_u)\)\ \((c\_u\%2 - 
                    s\_u\%2)\) - x, \ 
            2  c\_u\ \ s\_u\ \((2 + c\_u\ \ s\_t - 2  c\_t\ s\_t\ s\_u)\) - 
              y, 2  c\_t\ c\_u\ s\_t + s\_t\ s\_u - z, c\_u\%2 + s\_u\%2 - 1, 
            c\_t\%2 + s\_t\%2 - 1}, {x, y, z}, {c\_u, s\_u, c\_t, s\_t}, 
	
          MonomialOrder -> 
            EliminationOrder]\)[[1]]\)

\(\(Show[
      Graphics3D[
		
        Apply[{#1\ Cos[#2], #1\ Sin[#2], #3}&, 
			
          Cases[ContourPlot3D[
              Evaluate[
                klein /. {x -> r\ Cos[φ], 
                    y -> r\ Sin[φ]}], 

              				{r, 0.6, 3.3}, {φ, 0, 2  π}, {z, \ 
                \(-1.3\), \ 1.3}, 
				PlotPoints -> {12, 32, 16}, 
              MaxRecursion -> 0, \ 
              DisplayFunction\  -> \ Identity], _Polygon, \ Infinity], 
          \ {\(-2\)}]]]; \)\)