diff --git a/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeFace_2.h b/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeFace_2.h
index e1c6f2c3023..4edbc836b4f 100644
--- a/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeFace_2.h
+++ b/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeFace_2.h
@@ -3,12 +3,15 @@
 \ingroup PkgAlphaShape2Concepts
 \cgalConcept
 
-\cgalRefines `TriangulationFaceBase_2` 
+The concept `AlphaShapeFace_2` describes the requirements for the base face of an alpha shape.
 
-\cgalHasModel `CGAL::Alpha_shape_face_base_2`
+\cgalRefines `TriangulationFaceBase_2`, if the underlying triangulation of the alpha shape is a Delaunay triangulation.
+\cgalRefines `RegularTriangulationFaceBase_2`, if the underlying triangulation of the alpha shape is a regular triangulation.
+\cgalRefines `Periodic_2TriangulationFaceBase_2`, if the underlying triangulation of the alpha shape is a periodic triangulation.
+
+\cgalHasModel `CGAL::Alpha_shape_face_base_2` (templated with the appropriate triangulation face base class).
 
 */
-
 class AlphaShapeFace_2 {
 public:
 
diff --git a/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeVertex_2.h b/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeVertex_2.h
index 630e4a2481b..e0224242fc9 100644
--- a/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeVertex_2.h
+++ b/Alpha_shapes_2/doc/Alpha_shapes_2/Concepts/AlphaShapeVertex_2.h
@@ -3,9 +3,13 @@
 \ingroup PkgAlphaShape2Concepts
 \cgalConcept
 
-\cgalRefines `TriangulationVertexBase_2` 
+The concept `AlphaShapeVertex_2` describes the requirements for the base vertex of an alpha shape.
 
-\cgalHasModel `CGAL::Alpha_shape_vertex_base_2`
+\cgalRefines `TriangulationVertexBase_2`, if the underlying triangulation of the alpha shape is a Delaunay triangulation.
+\cgalRefines `RegularTriangulationVertexBase_2`, if the underlying triangulation of the alpha shape is a regular triangulation.
+\cgalRefines `Periodic_2TriangulationVertexBase_2`, if the underlying triangulation of the alpha shape is a periodic triangulation.
+
+\cgalHasModel `CGAL::Alpha_shape_vertex_base_2` (templated with the appropriate triangulation vertex base class).
 */
 class AlphaShapeVertex_2 {
 public: