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diff --git a/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation.h b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation.h
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+/*    This file is part of the Gudhi Library. The Gudhi library
+ *    (Geometric Understanding in Higher Dimensions) is a generic C++
+ *    library for computational topology.
+ *
+ *    Author(s):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2019 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef COXETER_TRIANGULATION_H_
+#define COXETER_TRIANGULATION_H_
+
+#include <stack>
+#include <map>
+#include <numeric> //iota
+
+#include <boost/range/iterator_range.hpp>
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+
+#include <Eigen/Eigenvalues>
+#include <Eigen/Sparse>
+#include <Eigen/SVD>
+
+#include <gudhi/Freudenthal_triangulation.h>
+#include <gudhi/Permutahedral_representation.h>
+
+namespace Gudhi {
+  
+namespace coxeter_triangulation {
+
+/** 
+ * \class Coxeter_triangulation
+ * \brief A class that stores Coxeter triangulation of type \f$\tilde{A}_d\f$.
+ * This triangulation has the greatest simplex quality out of all linear transformations
+ * of the Freudenthal-Kuhn triangulation.
+ *
+ * \ingroup coxeter_triangulation
+ *
+ * \tparam Permutahedral_representation_ Type of a simplex given by a permutahedral representation.
+ *  Needs to be a model of SimplexInCoxeterTriangulation.
+ */
+template <class Permutahedral_representation_
+	  = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > > >
+class Coxeter_triangulation : public Freudenthal_triangulation<Permutahedral_representation_> {
+
+  typedef Eigen::MatrixXd Matrix;
+
+  Matrix root_matrix(unsigned d) {
+    Matrix cartan(d,d);
+    for (unsigned i = 0; i < d; i++) {
+      cartan(i,i) = 1.0;
+    }
+    for (unsigned i = 1; i < d; i++) {
+      cartan(i-1,i) = -0.5;
+      cartan(i,i-1) = -0.5;
+    }
+    for (unsigned i = 0; i < d; i++)
+      for (unsigned j = 0; j < d; j++)
+	if (j+1 < i || j > i+1) 
+	  cartan(i,j) = 0;    
+    Eigen::SelfAdjointEigenSolver<Matrix> saes(cartan);
+    Eigen::VectorXd sqrt_diag(d);
+    for (unsigned i = 0; i < d; ++i)
+      sqrt_diag(i) = std::sqrt(saes.eigenvalues()[i]);
+
+    Matrix lower(d,d);
+    for (unsigned i = 0; i < d; i++)
+      for (unsigned j = 0; j < d; j++)
+	if (i < j)
+	  lower(i,j) = 0;
+	else
+	  lower(i,j) = 1;    
+    Matrix result = (lower * saes.eigenvectors()*sqrt_diag.asDiagonal()).inverse();
+    return result;
+  }
+  
+public:
+
+  /** \brief Constructor of Coxeter triangulation of a given dimension. 
+   * @param[in] dimension The dimension of the triangulation.
+   */
+  Coxeter_triangulation(std::size_t dimension)
+    : Freudenthal_triangulation<Permutahedral_representation_>(dimension, root_matrix(dimension)) {}
+};
+
+} // namespace coxeter_triangulation
+
+} // namespace Gudhi
+
+#endif