The statue is of the Hermes Logios type, Hermes as the god of eloquence. It is a late 1st century AD copy of a 5th century BC original.
The hallways of the Vatican are literally crowded with chipped, knicked, and scuffed
statuary. Nonetheless, these herma are in better shape than most.
This one claims to be a female figure
from 3600 BC. There's something not entirely female
about this piece to my eye.
This area of the museum was technically closed, but I was able to get a photo or two by wiggling my camera around the glass barrier. Before stone carving becamse popular, the ancients of this area did their art in terra cotta. The anthropomorphic statues were done in pieces, which were then fitted together. This was an entire room full of pieces in cabinets. The ones on the far left and bottom are unidentifiable to me - they looked more like abstract representations of the digestive tract than any external part. However, the other pieces in this cabinet were pretty easy to figure out.
The style of this piece really is reminescent of a modern cartoon for me. And, indeed, the beautiful woman refusing the Satyr is a comedic theme in ancient Rome. Unfortunately, I don't have any information on the history of this piece, but it is genuinely ancient. Some things don't change.