diff --git a/benchmarks/2d/periodic_affine.geo b/benchmarks/2d/periodic_affine.geo
index 5dcb666390166ee785b21d9cd29051e0194cd505..071a6d0ada9e3e11ea099579700fefaefdefa7bb 100644
--- a/benchmarks/2d/periodic_affine.geo
+++ b/benchmarks/2d/periodic_affine.geo
@@ -141,6 +141,6 @@ Volume(195) = {194};
 
 //Conditions maitre-esclave : ici en utilisant une transformation affine explicite
 //---------------------------
-Periodic Surface {168} = {54} Using {1,0,0,0, 0,-1,0,0, 0,0,-1,0, 0,0,0,1};
+Periodic Surface {168} = {54} Affine {1,0,0,0, 0,-1,0,0, 0,0,-1,0, 0,0,0,1};
 
 Characteristic Length{13} = 0.02;
diff --git a/benchmarks/3d/PeriodicRotationAndTranslation.geo b/benchmarks/3d/PeriodicRotationAndTranslation.geo
index cf628b3c8f2b4d85c15f10cdff40c0b807e8c3b1..c41f3a479ba9b869640b4e6a04ea9cbea3dec4de 100644
--- a/benchmarks/3d/PeriodicRotationAndTranslation.geo
+++ b/benchmarks/3d/PeriodicRotationAndTranslation.geo
@@ -24,9 +24,6 @@ Extrude {{0, 1, 0}, {-R_rotation, 0, 0}, Pi/4} {
 }
 
 Periodic Surface 28 {8, 9, 10, 11} = 6 {1, 2, 3, 4} ;
+Periodic Surface 50 {30, 31, 32, 33} = 6 {1, 2, 3, 4} ;
 
-// This fails with the new code:
-
-// Periodic Surface 50 {30, 31, 32, 33} = 6 {1, 2, 3, 4} ;
-
-// Periodic Surface {50} = {6} Rotate { {0, 1, 0}, {-R_rotation, 0, 0}, Pi/3} ;
+//Periodic Surface {50} = {6} Rotate { {0, 1, 0}, {-R_rotation, 0, 0}, Pi/3} ;
diff --git a/doc/texinfo/gmsh.texi b/doc/texinfo/gmsh.texi
index b8ba3ede049a0cc4109626dd006a4034fff92f33..a05660118ef450a650425d820d79865babdc73cb 100644
--- a/doc/texinfo/gmsh.texi
+++ b/doc/texinfo/gmsh.texi
@@ -2903,11 +2903,11 @@ the mesh of the surface.
 Force mesh of lines on the left-hand side (slaves) to match the mesh of
 the lines on the right-hand side (masters).
 
-@item Periodic Surface @var{expression} @{ @var{expression-list} @} = @var{expression} @{ @var{expression-list} @} < Using  @{ @var{expression-list} @} >;
+@item Periodic Surface @var{expression} @{ @var{expression-list} @} = @var{expression} @{ @var{expression-list} @} < Affine  @{ @var{expression-list} @} >;
 Force mesh of the surface on the left-hand side (slave, with boundary
 edges specified between braces) to match the mesh of the surface on the
 right-hand side (master, with boundary edges specified between braces). The
-optional @code{Using} list specifies an explicit affine transform (as a 4 x 4
+optional @code{Affine} list specifies an explicit affine transform (as a 4 x 4
 matrix given by row).
 
 @item Coherence Mesh;