Drawing Optical Lenses for Ray Tracing

Question

I am really new to optical system engineering and I am trying to do some very basic ray tracing through biconvex and biconcave lenses to understand how all of it works. I know there are tools such as OpticStudio etc, but I just want to code something up really simple to get my hands dirty with it.

Here is the issue I am running into. Consider a biconvex lens that has left surface and right surface with radii 1.628cm and 27.57cm respectively (-27.57 if we are following conventions). The thickness of the lens at the center is 0.357cm.

I am trying to draw this lenses on a plot using MATLAB. Since, these are spherical surfaces, I am basically drawing this lens as the intersection of two circles.

The question I have is, does the radii of the two surfaces and the thickness automatically constrain the height of the lens? Reason I ask this is that I am getting a maximum lens height of ~1.2cm.

Is this really how tall a lens with these parameters can be? Am I missing something really fundamental?