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diff --git a/src/Coxeter_triangulation/test/freud_triang_test.cpp b/src/Coxeter_triangulation/test/freud_triang_test.cpp
new file mode 100644
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+++ b/src/Coxeter_triangulation/test/freud_triang_test.cpp
@@ -0,0 +1,114 @@
+/*    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
+ */
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "freudenthal_triangulation"
+#include <boost/test/unit_test.hpp>
+
+#include <gudhi/Unitary_tests_utils.h>
+#include <gudhi/Freudenthal_triangulation.h>
+#include <gudhi/Coxeter_triangulation.h>
+
+BOOST_AUTO_TEST_CASE(freudenthal_triangulation) {
+  // Point location check
+  typedef std::vector<double> Point;
+  typedef Gudhi::coxeter_triangulation::Freudenthal_triangulation<> FK_triangulation;
+  typedef typename FK_triangulation::Simplex_handle Simplex_handle;
+  typedef typename FK_triangulation::Vertex_handle Vertex_handle;
+  typedef typename Simplex_handle::OrderedSetPartition Ordered_set_partition;
+  typedef typename Ordered_set_partition::value_type Part;
+
+  FK_triangulation tr(3);
+
+  // Point location check
+  {
+    Point point({3, -1, 0});
+    Simplex_handle s = tr.locate_point(point);
+    BOOST_CHECK(s.vertex() == Vertex_handle({3, -1, 0}));
+    BOOST_CHECK(s.partition() == Ordered_set_partition({Part({0, 1, 2, 3})}));
+  }
+
+  {
+    Point point({3.5, -1.5, 0.5});
+    Simplex_handle s = tr.locate_point(point);
+    BOOST_CHECK(s.vertex() == Vertex_handle({3, -2, 0}));
+    BOOST_CHECK(s.partition() == Ordered_set_partition({Part({0, 1, 2}), Part({3})}));
+  }
+
+  {
+    Point point({3.5, -1.8, 0.5});
+    Simplex_handle s = tr.locate_point(point);
+    BOOST_CHECK(s.vertex() == Vertex_handle({3, -2, 0}));
+    BOOST_CHECK(s.partition() == Ordered_set_partition({Part({0, 2}), Part({1}), Part({3})}));
+  }
+
+  {
+    Point point({3.5, -1.8, 0.3});
+    Simplex_handle s = tr.locate_point(point);
+    BOOST_CHECK(s.vertex() == Vertex_handle({3, -2, 0}));
+    BOOST_CHECK(s.partition() == Ordered_set_partition({Part({0}), Part({2}), Part({1}), Part({3})}));
+  }
+
+  // Dimension check
+  BOOST_CHECK(tr.dimension() == 3);
+  // Matrix check
+  Eigen::MatrixXd default_matrix = Eigen::MatrixXd::Identity(3, 3);
+  BOOST_CHECK(tr.matrix() == default_matrix);
+  // Vector check
+  Eigen::MatrixXd default_offset = Eigen::VectorXd::Zero(3);
+  BOOST_CHECK(tr.offset() == default_offset);
+
+  // Barycenter check
+  Point point({3.5, -1.8, 0.3});
+  Simplex_handle s = tr.locate_point(point);
+  Eigen::Vector3d barycenter_cart = Eigen::Vector3d::Zero();
+  for (auto v : s.vertex_range())
+    for (std::size_t i = 0; i < v.size(); i++) barycenter_cart(i) += v[i];
+  barycenter_cart /= 4.;  // simplex is three-dimensional
+  Eigen::Vector3d barycenter = tr.barycenter(s);
+  for (std::size_t i = 0; (long int)i < barycenter.size(); i++)
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(barycenter(i), barycenter_cart(i), 1e-7);
+
+  // Barycenter check for twice the scale
+  s = tr.locate_point(point, 2);
+  barycenter_cart = Eigen::Vector3d::Zero();
+  for (auto v : s.vertex_range())
+    for (std::size_t i = 0; i < v.size(); i++) barycenter_cart(i) += v[i];
+  barycenter_cart /= 3.;  // simplex is now a two-dimensional face
+  barycenter_cart /= 2.;  // scale
+  barycenter = tr.barycenter(s, 2);
+  for (std::size_t i = 0; (long int)i < barycenter.size(); i++)
+    GUDHI_TEST_FLOAT_EQUALITY_CHECK(barycenter(i), barycenter_cart(i), 1e-7);
+
+  // Matrix and offset change check
+  Eigen::MatrixXd new_matrix(3, 3);
+  new_matrix << 1, 0, 0, -1, 1, 0, -1, 0, 1;
+  Eigen::Vector3d new_offset(1.5, 1, 0.5);
+  tr.change_matrix(new_matrix);
+  tr.change_offset(new_offset);
+
+  BOOST_CHECK(tr.matrix() == new_matrix);
+  BOOST_CHECK(tr.offset() == new_offset);
+}
+
+#ifdef GUDHI_DEBUG
+BOOST_AUTO_TEST_CASE(freudenthal_triangulation_exceptions_in_debug_mode) {
+  // Point location check
+  typedef Gudhi::coxeter_triangulation::Freudenthal_triangulation<> FK_triangulation;
+
+  BOOST_CHECK_THROW (FK_triangulation tr(3, Eigen::MatrixXd::Identity(3, 3), Eigen::VectorXd::Zero(4)),
+                     std::invalid_argument);
+
+  FK_triangulation tr(3);
+  // Point of dimension 4
+  std::vector<double> point({3.5, -1.8, 0.3, 4.1});
+  BOOST_CHECK_THROW (tr.locate_point(point), std::invalid_argument);
+}
+#endif