This was a simple project done with a chunk of 5/8 steel rod.  the total size of the burner is no more than an inch tall.  The base is sufficiently heavy to prevent tipping of the incense when installed into the burner.

I began by facing the rod to provide a flat surface for drilling.  After the end was faced, I used a center drill to start the hole for the 7/64 drill.  I then drilled the 7/64 hole about 3/4 of an inch deep.  After then hole was drilled, I set the compound for 30 degrees and turned the taper.  I left a flat area of about 0.275 inches across the top ( see illustration ).  After the taper was cut, I knurled about 0.375 inches of the remaining 5/8 rod.  The knurling tool double tracked, but the knurl looks nice anyway.  After the knurl was applied, I used a cutoff tool to cut off the burner.  The burner bottom was then faced to create a very flat surface.

Then incense burner was put to immediate use!