The pyramid shape on diamond crystals are called trigons. They are very distinctive. They are most easily seen on the raw surface of a natural diamond.
Your Gem has completely smooth surfaces ie polished. Diamond is the hardest material, abrasion wise, on earth. It cannot be made completely smooth like that in a “natural or raw” state even with billions of years of weathering.
Your gem has all the characteristics of quartz.
Photos of trigons on a diamond crystal and a photo of my raw quartz specimen.