Yes fascinating inroads indeed... In fact I just read that the Moon and Star typically Othmanli decoration/insignis was not originally Muslim but in fact owes its origins further East in Hindu roots going much further back with the moon at the bottom of the diagram …
Here is a further link to Indian Crescent moon structures at
http://www.sikhmuseum.com/nishan/mistaken/crescent.html …
My other point here was to look at the hilt which also tends to illustrate cogs...but I needed other examples of this decoration...and perhaps this is only artistic impressions of geometric floral style. See Below.