I've located two historic measured drawings for the Edison Diamond Disc 
phonograph diamond stylus.  Scanned photocopies are here:

The June 28, 1917 drawing shows a tolerance of 0.00375 inch (3.75 mil) 
maximum radius to 0.0035 inch (3.5 mil) minimum radius.  The October 25, 
1916 drawing shows a 0.0035 inch (3.5 mil) radius with a 60 degree angle 

Expert Stylus Co. offers a 0.0037 inch (3.7 mil) radius spherical stylus 
for Diamond Discs.  The owner of the company told me that this size was 
based on measurements he took from an actual Edison Diamond Disc 
phonograph reproducer.  I have tried this Expert 0.0037 inch radius 
Diamond Discs stylus, mounted on a Stanton 500 cartridge, playing 
electrically.  It doesn't sound right to me.  I hear unnecessary noise.

For electrical playback of Diamond Discs, I've had the most consistent 
luck with a 0.0020 inch (2.0 mil) radius spherical size.  This is based on 
what sounds best to my ears, not based on objective measurements. 
Results can vary from disc to disc, so try different sizes.  

In general, I'd say that it doesn't make sense to use truncated styli on 
vertical cut records, since the information is on the bottom.   A good 
argument can be made for using elliptical shapes.   Beyond Diamond Discs, 
when playing wax or other soft material records with non-standard 
sizes/shapes, one should always be extremely wary of causing wear damage.

-Jerry Fabris, Museum Curator
Thomas Edison National Historical Park
West Orange, NJ