Whereas a thread that starts in only one position will take several twists of the cap to remove it, a triple start thread will achieve it in one or two, which is a highly desirable feature in a capped pen.
We also have corresponding plug (US - bottoming) taps for several of the sizes of we offer, which are available to buy separately. If the cap you're making is opaque, a plug (bottoming) tap will usually not be required, but if the material is translucent or clear, the thread will be visible from the outside - a plug (bottoming) tap will allow the thread to be cut with a clean stop to it.
Be sure to order the correct taps though. You need to know that thread taps are named differently depending on where you live:
UK starter = US taper
UK intermediate = US plug
UK plug = US bottoming
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