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diff --git a/src/Coxeter_triangulation/concept/SimplexInCoxeterTriangulation.h b/src/Coxeter_triangulation/concept/SimplexInCoxeterTriangulation.h
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+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2019 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef CONCEPT_COXETER_TRIANGULATION_SIMPLEX_IN_COXETER_TRIANGULATION_H_
+#define CONCEPT_COXETER_TRIANGULATION_SIMPLEX_IN_COXETER_TRIANGULATION_H_
+
+#include <cstdlib>  // for std::size_t
+
+#include <gudhi/Permutahedral_representation.h>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+/** \brief The concept SimplexInCoxeterTriangulation describes the requirements
+ * for a type to implement a representation of simplices in Freudenthal_triangulation
+ * or in Coxeter_triangulation.
+ */
+struct SimplexInCoxeterTriangulation {
+  /** \brief Type of the vertex. */
+  typedef Vertex_ Vertex;
+
+  /** \brief Type of the ordered partition. */
+  typedef Ordered_set_partition_ OrderedSetPartition;
+
+  /** \brief Dimension of the simplex. */
+  unsigned dimension() const;
+
+  /** \brief Type of a range of vertices, each of type Vertex. */
+  typedef Vertex_range;
+
+  /** \brief Returns a range of vertices of the simplex.
+   */
+  Vertex_range vertex_range() const;
+
+  /** \brief Type of a range of faces, each of type that
+   *  is a model of the concept SimplexInCoxeterTriangulation.
+   */
+  typedef Face_range;
+
+  /** \brief Returns a range of permutahedral representations of k-dimensional faces
+   *   of the simplex for some given integer parameter 'k'.
+   */
+  Face_range face_range(std::size_t k) const;
+
+  /** \brief Returns a range of permutahedral representations of facets of the simplex.
+   * The dimension of the simplex must be strictly positive.
+   */
+  Face_range facet_range() const;
+
+  /** \brief Type of a range of cofaces, each of type that
+   *  is a model of the concept SimplexInCoxeterTriangulation.
+   */
+  typedef Coface_range;
+
+  /** \brief Returns a range of permutahedral representations of k-dimensional cofaces
+   *   of the simplex for some given integer parameter 'k'.
+   */
+  Coface_range coface_range(std::size_t k) const;
+
+  /** \brief Returns a range of permutahedral representations of cofacets of the simplex.
+   * The dimension of the simplex must be strictly different from the ambient dimension.
+   */
+  Coface_range cofacet_range() const;
+
+  /** \brief Returns true, if the simplex is a face of other simplex. */
+  bool is_face_of(const Permutahedral_representation& other) const;
+};
+
+}  // namespace coxeter_triangulation
+
+}  // namespace Gudhi
+
+#endif