diff --git a/src/kernel/matrix.lisp b/src/kernel/matrix.lisp
index 79a4aa9..ba926f7 100644
--- a/src/kernel/matrix.lisp
+++ b/src/kernel/matrix.lisp
@@ -310,6 +310,6 @@
       (p-set! point tx ty tz))))
 
 (defun transform-points! (points matrix)
-  (mapc #'(lambda (p) (transform-point! p matrix)) points)
-  points)
+  (loop for p across points
+        do (transform-point! p matrix)))
 
diff --git a/src/kernel/point-cloud.lisp b/src/kernel/point-cloud.lisp
index 1ab6b69..bd8b729 100644
--- a/src/kernel/point-cloud.lisp
+++ b/src/kernel/point-cloud.lisp
@@ -23,6 +23,10 @@
 (defun make-point-cloud (points)
   (make-instance 'point-cloud :points points))
 
+(defmethod freeze-transform ((p-cloud point-cloud))
+  (transform-points! (points p-cloud) (transform-matrix (transform p-cloud)))
+  (reset-transform (transform p-cloud)))
+
 ;;; point generator functions --------------------------------------------------
 
 (defun make-line-points (p1 p2 num-segments)
diff --git a/src/kernel/polyhedron.lisp b/src/kernel/polyhedron.lisp
index 59abe6c..358b61c 100644
--- a/src/kernel/polyhedron.lisp
+++ b/src/kernel/polyhedron.lisp
@@ -309,7 +309,7 @@
                      :name name
                      :mesh-type mesh-type)))
 
-(defun make-cut-cube-polyhedron (side &key (name nil) (mesh-type 'polyhedron))
+(defun make-cut-cube (side &key (name nil) (mesh-type 'polyhedron))
   (let ((r (* side 0.5))
         (-r (* side -0.5))
         (b (* side 0.3)))
diff --git a/test/demo-kernel.lisp b/test/demo-kernel.lisp
index a30892f..8105ef9 100644
--- a/test/demo-kernel.lisp
+++ b/test/demo-kernel.lisp
@@ -722,6 +722,40 @@ Display shape bounds, face-normals, and axes.
       (setf (show-bounds? sphere) t)
       (add-shapes *scene* (list circle sphere icos))))
 
+#|
+(Demo 21 kernel) freezing shapes ===============================================
+
+Freeze a shape by transforming its points.
+|#
+(progn
+  (defparameter *cube* (make-cube 2.0))
+  (with-clear-scene
+    (add-shapes *scene* (list
+                         (translate-by
+                          (make-group
+                           (list (rotate-by
+                                  (make-group
+                                   (list
+                                    (translate-by
+                                     *cube*
+                                     (p! 2.5 0 0))))
+                                  (p! 0 45 0))))
+                          (p! 0 2 0))))
+    (setf (show-axis *cube*) 3.0)))
+
+#|
+Hints:
+- Press 1 to turn off shaded view so you can see cube axis better.
+- Press 7 to turn off global axes display.
+
+Local freezing: transforms a point-based shape's points by its transform matrix
+and resets the transform.
+|#
+(progn
+  (format t "~%~%Before freeze: ~a~%" (points *cube*))
+  (freeze-transform *cube*)
+  (format t "After freeze: ~a~%" (points *cube*)))
+
 #|
 END ============================================================================
 |#