Autodesk Developer Network 2011
Autodesk
Geometry API
§FamilyInstance.HostFace - Access the reference to the host face of a family instance
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§Regeneration and geometry status -  If updated geometry has not been Regenerated before accessing, Element.Geometry throws exception
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§GeometryObject.GraphicsStyleId - Access to ElementId of family primitive’s GraphicsStyle
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§Edge.AsCurve() - Provide a curve that corresponds to the edge
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§Solid.ComputeCentroid - Calculate the centroid of a solid
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Reference corbelHostFace = corbel.HostFace;
We can now get the reference to the host face of family instance, or if the instance is placed on a work plane, the reference to the geometry face underlying the work plane.

Element.Geometry has been modified to throw an exception if an updated geometry has not been Regenerated before accessing it.

We can access the ElementId of family primitive’s GraphicsStyle

The Geometry API provides a curve that corresponds to a edge

And we can also calculate the centroid of a solid. This will correspond only with the center of gravity if the solid represents a homogeneous structure of a single material.