diff --git a/src/sage/geometry/lattice_polytope.py b/src/sage/geometry/lattice_polytope.py
index 9d2e434ceb2..00d95c86285 100644
--- a/src/sage/geometry/lattice_polytope.py
+++ b/src/sage/geometry/lattice_polytope.py
@@ -117,6 +117,7 @@
 
 from sage.misc.lazy_import import lazy_import
 from sage.features import PythonModule
+from sage.features.palp import PalpExecutable
 lazy_import('ppl', ['C_Polyhedron', 'Generator_System', 'Linear_Expression'],
                     feature=PythonModule("ppl", spkg="pplpy"))
 lazy_import('ppl', 'point', as_='PPL_point',
@@ -146,6 +147,7 @@
 from collections.abc import Hashable
 from copyreg import constructor as copyreg_constructor
 import os
+import shlex
 from subprocess import Popen, PIPE
 from warnings import warn
 from functools import reduce
@@ -5105,6 +5107,11 @@ def _palp(command, polytopes, reduce_dimension=False):
     if _palp_dimension is not None:
         dot = command.find(".")
         command = command[:dot] + "-%dd" % _palp_dimension + command[dot:]
+    executable, args = command.split(" ", 1)
+    if executable.endswith('.x'):
+        executable = executable[:-2]
+    executable = PalpExecutable(executable).absolute_filename()
+    command = " ".join([shlex.quote(executable), args])
     input_file_name = tmp_filename()
     input_file = open(input_file_name, "w")
     for p in polytopes:
diff --git a/src/sage/geometry/polyhedron/palp_database.py b/src/sage/geometry/polyhedron/palp_database.py
index 873e6d290cc..70864270966 100644
--- a/src/sage/geometry/polyhedron/palp_database.py
+++ b/src/sage/geometry/polyhedron/palp_database.py
@@ -35,6 +35,7 @@
 
 from sage.structure.sage_object import SageObject
 from sage.rings.integer_ring import ZZ
+from sage.features.palp import PalpExecutable
 
 from sage.interfaces.process import terminate
 
@@ -134,7 +135,7 @@ def _palp_Popen(self):
             <...Popen...>
         """
 
-        return Popen(["class.x", "-b2a", "-di", self._data_basename],
+        return Popen([PalpExecutable("class").absolute_filename(), "-b2a", "-di", self._data_basename],
                      stdout=PIPE, encoding='utf-8', errors='surrogateescape')
 
     def _read_vertices(self, stdout, rows, cols):
@@ -459,7 +460,7 @@ def _palp_Popen(self):
             <...Popen...>
         """
 
-        return Popen(['class-4d.x', '-He',
+        return Popen([PalpExecutable('class-4d').absolute_filename(), '-He',
                       'H{}:{}L100000000'.format(self._h21, self._h11),
                       '-di', self._data_basename], stdout=PIPE,
                      encoding='utf-8', errors='surrogateescape')