Revit uses a variety of curve types to represent face geometry in a document. These include:
| 
 Face type  | 
 Revit API class  | 
 Definition  | 
 Notes  | 
| 
 Plane  | 
 PlanarFace  | 
 A plane defined by the origin and unit vectors in U and V.  | 
|
| 
 Cylinder  | 
 CylindricalFace  | 
 A face defined by extruding a circle along an axis.  | 
 .Radius provides the “radius vectors” – the unit vectors of the circle multiplied by the radius value.  | 
| 
 Cone  | 
 ConicalFace  | 
 A face defined by rotation of a line about an axis.  | 
 .Radius provides the “radius vectors” – the unit vectors of the circle multiplied by the radius value.  | 
| 
 Revolved face  | 
 RevolvedFace  | 
 A face defined by rotation of an arbitrary curve about an axis.  | 
 .Radius provides the unit vectors of the plane of rotation, there is no “radius” involved.  | 
| 
 Ruled surface  | 
 RuledFace  | 
 A face defined by sweeping a line between two profile curves, or one profile curve and one point.  | 
 Both curve(s) and point(s) can be obtained as properties.  | 
| 
 Hermite face  | 
 HermiteFace  | 
 A face defined by Hermite interpolation between points.  | 
Mathematical representations of all of the Revit face types can be found here.