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diff --git a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/face_from_indices.h b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/face_from_indices.h
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+++ b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/face_from_indices.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 PERMUTAHEDRAL_REPRESENTATION_FACE_FROM_INDICES_H_
+#define PERMUTAHEDRAL_REPRESENTATION_FACE_FROM_INDICES_H_
+
+#include <cstdlib>  // for std::size_t
+#include <algorithm>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+/** \brief Computes the permutahedral representation of a face of a given simplex
+ *  and a range of the vertex indices that compose the face.
+ *
+ * \tparam Permutahedral_representation has to be Permutahedral_representation
+ * \tparam Index_range is a range of unsigned integers taking values in 0,...,k,
+ * where k is the dimension of the simplex simplex.
+ *
+ * @param[in] simplex Input simplex.
+ * @param[in] indices Input range of indices.
+ */
+template <class Permutahedral_representation, class Index_range>
+Permutahedral_representation face_from_indices(const Permutahedral_representation& simplex,
+                                               const Index_range& indices) {
+  using range_index = typename Index_range::value_type;
+  using Ordered_set_partition = typename Permutahedral_representation::OrderedSetPartition;
+  using Part = typename Ordered_set_partition::value_type;
+  using part_index = typename Part::value_type;
+  Permutahedral_representation value;
+  std::size_t d = simplex.vertex().size();
+  value.vertex() = simplex.vertex();
+  std::size_t k = indices.size() - 1;
+  value.partition().resize(k + 1);
+  std::size_t l = simplex.partition().size() - 1;
+  for (std::size_t h = 1; h < k + 1; h++)
+    for (range_index i = indices[h - 1]; i < indices[h]; i++)
+      for (part_index j : simplex.partition()[i]) value.partition()[h - 1].push_back(j);
+  for (range_index i = indices[k]; i < l + 1; i++)
+    for (part_index j : simplex.partition()[i]) value.partition()[k].push_back(j);
+  for (range_index i = 0; i < indices[0]; i++)
+    for (part_index j : simplex.partition()[i]) {
+      if (j != d)
+        value.vertex()[j]++;
+      else
+        for (std::size_t l = 0; l < d; l++) value.vertex()[l]--;
+      value.partition()[k].push_back(j);
+    }
+  // sort the values in each part (probably not needed)
+  for (auto& part : value.partition()) std::sort(part.begin(), part.end());
+  return value;
+}
+
+}  // namespace coxeter_triangulation
+
+}  // namespace Gudhi
+
+#endif