It's pretty much just a cone - most likely triangular/slightly trapezoidal piece(s). I'd take some muslin fabric and fuss with it until I got the shape how I wanted it.
, not quite what you want, you want a point in the back.
It will depend on how big you want it in comparison to your face. You can put craft foam or interfacing around the top so that it stands up nicely on its own.
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan