// find the name of the GraphicsSytleCategory for every geometric primitive in a family instance
        Options options = app.Create.NewGeometryOptions();
        GeometryElement geomElem = element.get_Geometry(options);
        foreach (GeometryObject geomObj in geomElem)
        {
            GeometryInstance geomInst = geomObj as GeometryInstance;
            if (geomInst != null)
            {
                foreach (Object obj in geomInst.SymbolGeometry)
                {
                    GeometryObject geomObject = obj as GeometryObject;
                    GraphicsStyle gStyle = doc.GetElement(geomObject.GraphicsStyleId) as GraphicsStyle;
                    if (gStyle != null)
                    {
                        string gstyleName = gStyle.GraphicsStyleCategory.Name;
                    }
                }
            }
        }

' find the name of the GraphicsSytleCategory for every geometric primitive in a family instance
Dim options As Options = app.Create.NewGeometryOptions()
Dim geomElem As GeometryElement = element.Geometry(options)
For Each geomObj As GeometryObject In geomElem
    Dim geomInst As GeometryInstance = TryCast(geomObj, GeometryInstance)
    If geomInst IsNot Nothing Then
        For Each obj As [Object] In geomInst.SymbolGeometry
            Dim geomObject As GeometryObject = TryCast(obj, GeometryObject)
            Dim gStyle As GraphicsStyle = TryCast(doc.GetElement(geomObject.GraphicsStyleId), GraphicsStyle)
            If gStyle IsNot Nothing Then
                Dim gstyleName As String = gStyle.GraphicsStyleCategory.Name
            End If
        Next
    End If