diff --git a/Polygon/doc_tex/Polygon/polygon.tex b/Polygon/doc_tex/Polygon/polygon.tex
index 2a026f304ce..e289327c920 100644
--- a/Polygon/doc_tex/Polygon/polygon.tex
+++ b/Polygon/doc_tex/Polygon/polygon.tex
@@ -29,7 +29,7 @@ Currently, the \ccc{Polygon_2} class is a nice wrapper around the algorithms,
 but little more. Especially, computed values are not cached.
 That is, when the \ccc{is_simple()} member function is called twice or more,
 the result is computed each time anew. It is possible to set a preprocessor flag
-to alter this behaviour. In the future, caching will become the default.
+to alter this behavior. In the future, caching will become the default.
 
 \section{Example}
 
diff --git a/Polygon/doc_tex/Polygon_ref/Polygon_2.tex b/Polygon/doc_tex/Polygon_ref/Polygon_2.tex
index 2215bd54a55..5e2f0b48260 100644
--- a/Polygon/doc_tex/Polygon_ref/Polygon_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/Polygon_2.tex
@@ -19,7 +19,7 @@
 \ccDefinition
   
 The class \ccRefName\ implements polygons.
-The \ccRefName\ is parameterised by a traits class and a container class.
+The \ccRefName\ is parameterized by a traits class and a container class.
 The latter can be any class that fulfills the requirements for an STL container.
 It defaults to the vector class.
 
@@ -199,7 +199,7 @@ circulators and iterators that allow to traverse the vertices and edges.
     { Returns the bottommost vertex of the polygon \ccStyle{p} with the smallest
      \ccStyle{x}-coordinate. }
     
-For convenience we provide the following boolean functions:    
+For convenience we provide the following Boolean functions:    
 \ccThree{Segment_2}{}{\hspace*{10cm}}
 
 \ccMethod{bool is_counterclockwise_oriented() const;}
diff --git a/Polygon/doc_tex/Polygon_ref/area_2.tex b/Polygon/doc_tex/Polygon_ref/area_2.tex
index 72bda2d757e..7f1444b066f 100644
--- a/Polygon/doc_tex/Polygon_ref/area_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/area_2.tex
@@ -41,7 +41,7 @@ returns the area instead of taking it as a parameter.
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
 	    \item \ccc{Compute_area_2} : Computes the signed area of the
diff --git a/Polygon/doc_tex/Polygon_ref/bbox_2.tex b/Polygon/doc_tex/Polygon_ref/bbox_2.tex
index 01b6b39234a..a7aab1b0495 100644
--- a/Polygon/doc_tex/Polygon_ref/bbox_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/bbox_2.tex
@@ -34,7 +34,7 @@ Returns the bounding box of the range \ccStyle{[first,last)}.
 %\ccIndexSubitem[C]{bbox_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  In fact, only the members \ccc{Construct_bbox_2} and
 	  \ccc{construct_bbox_2_object} are used.
     \item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2},
diff --git a/Polygon/doc_tex/Polygon_ref/bottom_vertex_2.tex b/Polygon/doc_tex/Polygon_ref/bottom_vertex_2.tex
index 68de8e97e3d..2ab341e8184 100644
--- a/Polygon/doc_tex/Polygon_ref/bottom_vertex_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/bottom_vertex_2.tex
@@ -36,7 +36,7 @@ with the smallest \ccStyle{x}-coordinate is taken.
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  In fact, only the members \ccc{Less_yx_2} and
 	  \ccc{less_yx_2_object} are used.
     \item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
diff --git a/Polygon/doc_tex/Polygon_ref/bounded_side_2.tex b/Polygon/doc_tex/Polygon_ref/bounded_side_2.tex
index 7779431a146..9f038a051fc 100644
--- a/Polygon/doc_tex/Polygon_ref/bounded_side_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/bounded_side_2.tex
@@ -42,7 +42,7 @@ According to the definition points in the bounded region are inside the polygon.
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
             \item \ccc{Compare_x_2}
diff --git a/Polygon/doc_tex/Polygon_ref/is_convex_2.tex b/Polygon/doc_tex/Polygon_ref/is_convex_2.tex
index ffbb2f56775..c6cb097108a 100644
--- a/Polygon/doc_tex/Polygon_ref/is_convex_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/is_convex_2.tex
@@ -33,7 +33,7 @@ const Traits& traits); }
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
             \item \ccc{Less_xy_2}
diff --git a/Polygon/doc_tex/Polygon_ref/is_simple_2.tex b/Polygon/doc_tex/Polygon_ref/is_simple_2.tex
index 969a00e4412..5a7987f3343 100644
--- a/Polygon/doc_tex/Polygon_ref/is_simple_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/is_simple_2.tex
@@ -39,7 +39,7 @@ range \ccc{first} \ldots\ \ccc{last} is simple.
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
             \item \ccc{Point_2}
diff --git a/Polygon/doc_tex/Polygon_ref/left_vertex_2.tex b/Polygon/doc_tex/Polygon_ref/left_vertex_2.tex
index fd9513c97b8..4f037894492 100644
--- a/Polygon/doc_tex/Polygon_ref/left_vertex_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/left_vertex_2.tex
@@ -36,7 +36,7 @@ with the smallest \ccStyle{y}-coordinate is taken.
 \ccIndexSubitem[C]{left_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  In fact, only the members \ccc{Less_xy_2} and
 	  \ccc{less_xy_2_object} are used.
     \item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
diff --git a/Polygon/doc_tex/Polygon_ref/orientation_2.tex b/Polygon/doc_tex/Polygon_ref/orientation_2.tex
index 81d8e298eed..c08800f2e54 100644
--- a/Polygon/doc_tex/Polygon_ref/orientation_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/orientation_2.tex
@@ -36,7 +36,7 @@ Orientation orientation_2(ForwardIterator first, ForwardIterator last,
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
             \item \ccc{Less_xy_2}
diff --git a/Polygon/doc_tex/Polygon_ref/oriented_side_2.tex b/Polygon/doc_tex/Polygon_ref/oriented_side_2.tex
index c53c71c085d..fe967c893be 100644
--- a/Polygon/doc_tex/Polygon_ref/oriented_side_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/oriented_side_2.tex
@@ -35,7 +35,7 @@ Oriented_side oriented_side_2(ForwardIterator first, ForwardIterator last,
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
             \item \ccc{Less_xy_2}
diff --git a/Polygon/doc_tex/Polygon_ref/polygon_area_2.tex b/Polygon/doc_tex/Polygon_ref/polygon_area_2.tex
index 0bfc42014ff..a0385c7e8ee 100644
--- a/Polygon/doc_tex/Polygon_ref/polygon_area_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/polygon_area_2.tex
@@ -38,7 +38,7 @@ clockwise polygons. If the polygon is not simple, the area is not well defined.
 \ccIndexSubitem[C]{bottom_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  Only the following members of this traits class are used:
           \begin{itemize}
 	    \item \ccc{Compute_area_2} : Computes the signed area of the
diff --git a/Polygon/doc_tex/Polygon_ref/right_vertex_2.tex b/Polygon/doc_tex/Polygon_ref/right_vertex_2.tex
index c5bf78f4efc..3ffef36bbc3 100644
--- a/Polygon/doc_tex/Polygon_ref/right_vertex_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/right_vertex_2.tex
@@ -36,7 +36,7 @@ with the largest \ccStyle{y}-coordinate is taken.
 \ccIndexSubitem[C]{right_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  In fact, only the members \ccc{Less_xy_2} and
 	  \ccc{less_xy_2_object} are used.
     \item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
diff --git a/Polygon/doc_tex/Polygon_ref/top_vertex_2.tex b/Polygon/doc_tex/Polygon_ref/top_vertex_2.tex
index ec9ee6ab68d..1109ca1791b 100644
--- a/Polygon/doc_tex/Polygon_ref/top_vertex_2.tex
+++ b/Polygon/doc_tex/Polygon_ref/top_vertex_2.tex
@@ -36,7 +36,7 @@ with the largest \ccStyle{x}-coordinate is taken.
 \ccIndexSubitem[C]{top_vertex_2}{requirements}
 \begin{enumerate}
     \item \ccc{Traits} is a model of the concept 
-	  PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
+	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
 	  In fact, only the members \ccc{Less_yx_2} and
 	  \ccc{less_yx_2_object} are used.
     \item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},