Some glass pushers may find that instead of a full or complete lap, they may want to try a star lap. Great...what star pattern to use? Here are two options.

FIRST OPTION. This may be a good starting point, and based on your personal technique and results you can make changes. (This pattern provides 100% lap action/contact area in the center, and gradually tapers to zero at the edges.)

An Excel spreadsheet generates the pattern, which you can print and use as a template in shaping your star lap. As you can see, from this screen grab, you only have to adjust two parameters: number of petals, and the 'petal power' which controls how rapidly an exponential function reduces the 100% action of the lap's center to 0% at the lap's edge.

Here are some examples of the patterns you can generate by changing 'petal power' and number of petals.

SECOND OPTION. This lap has minimum action at the .707 radius (the 70% zone, as some call it), and tapers off to zero at the center and edge. Why? Look at the following curve. It represents the 'difference' between a sphere and a paraboloid that have the same center and extreme edges...the deviation is greatest somewhere in the middle...actually at the .707 radius point. If you've looked at amateur mirror making texts you've probably seen this profile before, and if you've seen photos of a good paraboloid on a Foucalt test stand...this represents the 'donut profile' you're supposed to see when you null the 70% zone. So, one approach to parabolizing is to leave the 70% zone alone, and remove more glass at the edge and center.

OK, take this curve, and re-plot it in polar coordinates (took some head scratching to make this work in a spreadsheet) and you get....

I've colored in purple one of the five areas of the lap you should scrape away. Depending on your technique (and perhaps if you figure convex surfaces)...you might find this lap useful by making lap action at the 70% zone maximum instead of minimum...which means do the opposite of what I just told you. ;-) Some experimentation may be required to make this work well for you.

Which of these star laps do I prefer? Neither. If I can get away with it, I parabolize with subdiameter (with no star pattern) laps. I'll polish with a full size, or oversized lap, and then start parabolizing with a 60% subdiameter lap. If all goes as planned, the outer zones tend to parabolize first, and I'm left with a high center compared to the outer zones. If I can't bring the center to proper correction that agrees with the outer zones with the 60% lap, I'll use an even smaller subdiameter lap to parabolize the center.