added 
The IfcTriangulatedFaceSet is a tessellated face set with all faces being bound by triangles. The faces are constructed by implicit polylines defined by three Cartesian points. Depending on the value of the attribute Closed the instance of IfcTriangulatedFaceSet represents:
The coordinates of each point are provided by a onebased index into an ordered list of Cartesian points provided by the twodimensional list CoordIndex, where
Depending on the provision of PnIndex the indices point either directly into the IfcCartesianPointList3D referenced by Coordinates defined at the supertype IfcTessellatedFaceSet, or they point into the PnIndex where the integer values at that position provides the location of the coordinate values within the IfcCartesianPointList3D. See Figure 1 for the handling of point index.
See Figure 2 for using the IfcTriangulatedFaceSet without (as default) and with using the PnIndex.
Optionally normals can be provided. Only normals per vector are supported allowing for visually curved triangles when the three normals of the corresponding three vertices of a triangle are not colinear to the normal of the triangular face. If they are identical, normals shall be omited.
NOTE In case of a body representation having triangular faces with curvature, different normals for all three vertices in context of this triangles are exported, describing the curvature for smooth visualisation. In case of triangular faces with no curvature, the three vertexbased normals are identical and could always be computed from the face. Therefore vertices should only be exported to support smooth visualisation by curvature of triangles. In case of faceted representation no vertices should be exported.
Normals are provided by the twodimensional list Normals, where
The indices in the CoordIndex point into the list of Normals. The indices of CoordIndex are applied to both points, either directly directly, or via the PnIndex and normals. See Figure 3 for handling of normals.
NOTE Using corresponding lists of points and normals allows to use only a single list of indices into both at the expense of having nonunique collections of vertices.
Figure 4 shows the use of IfcTriangulatedFaceSet without annotation. The diagram of the IfcTriangulatedFaceSet represents the indices and the ordered list into which the indices point. The index starts with 1 (indexed as 1 to N), if the greatest index in CoordIndex in N, then the IfcCartesianPointList shall have N lists of 3:3 coordinates.
Figure 168 shows an IfcTriangulatedFaceSet represented by IfcCartesianPointList3D: ((0.,0.,0.), (1.,0.,0.), (1.,1.,0.), (0.,1.,0.), (0.,0.,2.), (1.,0.,2.), (1.,1.,2.), (0.,1.,2.)) 

Figure 4 — Triangulated face set geometry 
NOTE The definition of IfcTriangulatedFaceSet is based on the indexedFaceSet and indexedTriangleSet defined in ISO/IEC 197751. The use of PnIndex has been adopted from triangulated_surface_set defined in ISO1030342.
HISTORY New entity in IFC4.
Informal Propositions:
#  Attribute  Type  Description 

IfcRepresentationItem  
LayerAssignment  SET [0:1] OF IfcPresentationLayerAssignment FOR AssignedItems  Assignment of the representation item to a single or multiple layer(s). The LayerAssignments can override a LayerAssignments of the IfcRepresentation it is used within the list of Items. > IFC2x3 CHANGE The inverse attribute LayerAssignments has been added. > IFC4 CHANGE The inverse attribute LayerAssignment has been restricted to max 1. Upward compatibility for file based exchange is guaranteed.  
StyledByItem  SET [0:1] OF IfcStyledItem FOR Item  Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve. > IFC2x3 CHANGE The inverse attribute StyledByItem has been added.  
IfcGeometricRepresentationItem  
IfcTessellatedItem  
IfcTessellatedFaceSet  
1  Coordinates  IfcCartesianPointList3D  An ordered list of Cartesian points used by the coordinate index defined at the subtypes of IfcTessellatedFaceSet. 
Dim  INVALID  The space dimensionality of this geometric representation item, it is always 3.  
HasColours  SET [0:1] OF IfcIndexedColourMap FOR MappedTo  Reference to the indexed colour map providing the corresponding colour RGB values to the faces of the subtypes of IfcTessellatedFaceSet.  
HasTextures  SET [0:?] OF IfcIndexedTextureMap FOR MappedTo  Reference to the indexed texture map providing the corresponding texture coordinates to the vertices bounding the faces of the subtypes of IfcTessellatedFaceSet.  
IfcTriangulatedFaceSet  
2  Normals  OPTIONAL LIST [1:?] OF LIST [3:3] OF IfcParameterValue  An ordered list of three directions for normals. It is a twodimensional list of directions provided by three parameter values. * The first dimension corresponds to the vertex indices of the Coordindex * The second dimension has exactly three values, [1] the xdirection, [2] the ydirection and [3] the zdirections 
3  Closed  OPTIONAL IfcBoolean  Indication whether the IfcTriangulatedFaceSet is a closed shell or not. If omited no such information can be provided. 
4  CoordIndex  LIST [1:?] OF LIST [3:3] OF IfcPositiveInteger  Twodimensional list for the indexedbased triangles, where * The first dimension represents the triangles (from 1 to N) * The second dimension has exactly three values representing the indices to three vertex points (from 1 to 3). > NOTE The coordinates of the vertices are provided by the indexed list of _SELF\IfcTessellatedFaceSet.Coordinates.CoordList_. 
5  PnIndex  OPTIONAL LIST [1:?] OF IfcPositiveInteger  The list of integers defining the locations in the IfcCartesianPointList3D to obtain the point coordinates for the indices withint the CoordIndex. If the PnIndex is not provided the indices point directly into the IfcCartesianPointList3D. 
NumberOfTriangles  INVALID  Derived number of triangles used for this triangulation. 
ENTITY IfcTriangulatedFaceSet SUPERTYPE OF (ONEOF (IfcTriangulatedIrregularNetwork)) SUBTYPE OF (IfcTessellatedFaceSet); Normals : OPTIONAL LIST [1:?] OF LIST [3:3] OF IfcParameterValue; Closed : OPTIONAL IfcBoolean; CoordIndex : LIST [1:?] OF LIST [3:3] OF IfcPositiveInteger; PnIndex : OPTIONAL LIST [1:?] OF IfcPositiveInteger; DERIVE NumberOfTriangles : IfcInteger := SIZEOF(CoordIndex); END_ENTITY;