diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h b/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h
index aa057c46dfb..944d6e8ca23 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h
@@ -436,7 +436,6 @@ private:
                 eminp = intersection;
                 emin = eproj;
                 minp = from_exact(intersection);
-                //min = proj;
                 FT p = dir * edge_dir;
                 min_speed = CGAL::approximate_sqrt(edge_dir * edge_dir) / p;
               }
@@ -444,9 +443,7 @@ private:
                 emaxp = intersection;
                 emax = eproj;
                 maxp = from_exact(intersection);
-                //max = proj;
                 typename Intersection_kernel::FT p = dir * edge_dir;
-                CGAL_assertion(p != 0);
                 max_speed = CGAL::approximate_sqrt(edge_dir * edge_dir) / from_exact(p);
               }
             }
diff --git a/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_3.h b/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_3.h
index adc9caf8683..c414ec4a88f 100644
--- a/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_3.h
+++ b/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_3.h
@@ -1267,12 +1267,12 @@ private:
 
       if (pos && neg) {
         std::cout << "face is not convex" << std::endl;
-        exit(1);
+        CGAL_assertion(false);
       }
 
       if (!pos && !neg) {
         std::cout << "face is degenerated" << std::endl;
-        exit(1);
+        CGAL_assertion(false);
       }
 
       if (neg) {
diff --git a/Kinetic_space_partition/test/Kinetic_space_partition/CMakeLists.txt b/Kinetic_space_partition/test/Kinetic_space_partition/CMakeLists.txt
index 39ac1e88597..038b9fa4615 100644
--- a/Kinetic_space_partition/test/Kinetic_space_partition/CMakeLists.txt
+++ b/Kinetic_space_partition/test/Kinetic_space_partition/CMakeLists.txt
@@ -19,7 +19,7 @@ if(Boost_FOUND)
     message(STATUS "Found Eigen")
     include(CGAL_Eigen_support)
 
-  set(targets kinetic_3d_test_all)
+  set(targets kinetic_3d_test_all issue_8624)
 
     set(project_linked_libraries)
     set(project_compilation_definitions)
diff --git a/Kinetic_space_partition/test/Kinetic_space_partition/data/issue_8624.off b/Kinetic_space_partition/test/Kinetic_space_partition/data/issue_8624.off
new file mode 100644
index 00000000000..67cd2a1b0d0
--- /dev/null
+++ b/Kinetic_space_partition/test/Kinetic_space_partition/data/issue_8624.off
@@ -0,0 +1,777 @@
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\ No newline at end of file
diff --git a/Kinetic_space_partition/test/Kinetic_space_partition/issue_8624.cpp b/Kinetic_space_partition/test/Kinetic_space_partition/issue_8624.cpp
new file mode 100644
index 00000000000..1a3ddb7fc1e
--- /dev/null
+++ b/Kinetic_space_partition/test/Kinetic_space_partition/issue_8624.cpp
@@ -0,0 +1,80 @@
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Kinetic_space_partition_3.h>
+#include <CGAL/Real_timer.h>
+#include <CGAL/IO/polygon_soup_io.h>
+
+using EPICK = CGAL::Exact_predicates_inexact_constructions_kernel;
+using EPECK = CGAL::Exact_predicates_exact_constructions_kernel;
+
+using Kernel     = EPICK;
+using FT         = typename Kernel::FT;
+using Point_3    = typename Kernel::Point_3;
+
+using Surface_mesh = CGAL::Surface_mesh<Point_3>;
+using KSP          = CGAL::Kinetic_space_partition_3<EPICK>;
+using Timer        = CGAL::Real_timer;
+
+int main(int argc, char** argv)
+{
+  // Reading polygons from file
+  std::string input_filename = (argc > 1 ? argv[1] : "data/issue_8624.off");
+  std::ifstream input_file(input_filename);
+
+  std::vector<Point_3> input_vertices;
+  std::vector<std::vector<std::size_t> > input_faces;
+
+  if (CGAL::IO::read_polygon_soup(input_filename, input_vertices, input_faces)) {
+    std::cout << "* reading the file: " << input_filename << "!" << std::endl;
+    input_file.close();
+  } else {
+    std::cerr << "ERROR: can't read the file " << input_filename << "!" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  std::cout << "--- INPUT STATS: \n* number of polygons: " << input_faces.size() << std::endl;
+
+  // Parameters.
+  const unsigned int k = (argc > 2 ? std::atoi(argv[2]) : 1);
+
+  // Initialization of Kinetic_space_partition_3 object.
+  // 'debug' set to true exports intermediate results into files in the working directory.
+  // The resulting volumes are exported into a volumes folder, if the folder already exists.
+  KSP ksp(CGAL::parameters::verbose(true).debug(false));
+
+  // Providing input polygons.
+  ksp.insert(input_vertices, input_faces);
+
+  Timer timer;
+  timer.start();
+
+  // 'initialize' creates the intersection graph that is used for the partition.
+  ksp.initialize(CGAL::parameters::bbox_dilation_ratio(1.1).reorient_bbox(false));
+
+  // Creating the partition with allowing up to 'k' intersections for each kinetic polygon.
+  ksp.partition(k);
+
+  timer.stop();
+  const FT time = static_cast<FT>(timer.time());
+
+  // Access the kinetic partition via linear cell complex.
+  typedef CGAL::Linear_cell_complex_traits<3, EPECK> LCC_Traits;
+  CGAL::Linear_cell_complex_for_combinatorial_map<3, 3, LCC_Traits, typename KSP::Linear_cell_complex_min_items> lcc;
+  ksp.get_linear_cell_complex(lcc);
+
+  std::vector<unsigned int> cells = { 0, 2, 3 }, count;
+  count = lcc.count_cells(cells);
+
+  assert(count[0] != 0);
+  assert(count[2] != 0);
+  assert(count[3] != 0);
+
+  if (count[0] == 0 || count[2] == 0 || count[3] == 0)
+    return EXIT_FAILURE;
+
+  std::cout << "For k = " << k << ":\n" << " vertices: " << count[0] << "\n faces: " << count[2] << "\n volumes: " << count[3] << std::endl;
+
+  std::cout << "\n3D kinetic partition created in " << time << " seconds!" << std::endl;
+
+  return EXIT_SUCCESS;
+}