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Hi Sophie
The usual way to construct these 'vertical' paperweights it to make a conventional paperweight, then attach it on one side to a different pontil, knock off the first rod, then add glass which is turned into the foot. When the finished 'vertical' weight is knocked off the pontil, there is a pontil mark on the very top of the weight. Sometimes it is polished off, sometimes it remains - you can see it on some Ysart pedestal weight, and on some Belgian ones. If this Chinese one had a single facet on top, I would suggest it was just there to hide the pontil mark: but two together is odd, unless the pontil mark was that shape!
Alan