Photo Number 108

I believe this photo was taken in the late 1920's.  Does anyone know what this hat was called?   This is a South Dakota/Illinois photo.  It is not marked in anyway.   The trim on the house is very ornate..Larry will know exactly what it is called!
Thanks for stopping by, do come again:)
Update: 
Norkio says Gingerbread Trim..and just a hat! 
Larry says it is picket running trim.  There are different forms of these old trims.