diff --git a/cube.c b/cube.c
index 2bce1bd..bf24960 100644
--- a/cube.c
+++ b/cube.c
@@ -11,6 +11,8 @@
 
 #include "puzzles.h"
 
+#define PI 3.14159265358979323846264338327950884197169399
+
 #define MAXVERTICES 20
 #define MAXFACES 20
 #define MAXORDER 4
@@ -1002,7 +1004,11 @@ static void free_ui(game_ui *ui)
 {
 }
 
-static game_state *make_move(game_state *from, game_ui *ui,
+struct game_drawstate {
+    int ox, oy;                        /* pixel position of float origin */
+};
+
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
 			     int x, int y, int button)
 {
     int direction;
@@ -1016,7 +1022,9 @@ static game_state *make_move(game_state *from, game_ui *ui,
     button = button & (~MOD_MASK | MOD_NUM_KEYPAD);
 
     /*
-     * All moves are made with the cursor keys or numeric keypad.
+     * Moves can be made with the cursor keys or numeric keypad, or
+     * alternatively you can left-click and the polyhedron will
+     * move in the general direction of the mouse pointer.
      */
     if (button == CURSOR_UP || button == (MOD_NUM_KEYPAD | '8'))
         direction = UP;
@@ -1034,7 +1042,69 @@ static game_state *make_move(game_state *from, game_ui *ui,
         direction = UP_RIGHT;
     else if (button == (MOD_NUM_KEYPAD | '3'))
         direction = DOWN_RIGHT;
-    else
+    else if (button == LEFT_BUTTON) {
+        /*
+         * Find the bearing of the click point from the current
+         * square's centre.
+         */
+        int cx, cy;
+        double angle;
+
+        cx = from->squares[from->current].x * GRID_SCALE + ds->ox;
+        cy = from->squares[from->current].y * GRID_SCALE + ds->oy;
+
+        if (x == cx && y == cy)
+            return NULL;               /* clicked in exact centre!  */
+        angle = atan2(y - cy, x - cx);
+
+        /*
+         * There are three possibilities.
+         * 
+         *  - This square is a square, so we choose between UP,
+         *    DOWN, LEFT and RIGHT by dividing the available angle
+         *    at the 45-degree points.
+         * 
+         *  - This square is an up-pointing triangle, so we choose
+         *    between DOWN, LEFT and RIGHT by dividing into
+         *    120-degree arcs.
+         * 
+         *  - This square is a down-pointing triangle, so we choose
+         *    between UP, LEFT and RIGHT in the inverse manner.
+         * 
+         * Don't forget that since our y-coordinates increase
+         * downwards, `angle' is measured _clockwise_ from the
+         * x-axis, not anticlockwise as most mathematicians would
+         * instinctively assume.
+         */
+        if (from->squares[from->current].npoints == 4) {
+            /* Square. */
+            if (fabs(angle) > 3*PI/4)
+                direction = LEFT;
+            else if (fabs(angle) < PI/4)
+                direction = RIGHT;
+            else if (angle > 0)
+                direction = DOWN;
+            else
+                direction = UP;
+        } else if (from->squares[from->current].directions[UP] == 0) {
+            /* Up-pointing triangle. */
+            if (angle < -PI/2 || angle > 5*PI/6)
+                direction = LEFT;
+            else if (angle > PI/6)
+                direction = DOWN;
+            else
+                direction = RIGHT;
+        } else {
+            /* Down-pointing triangle. */
+            assert(from->squares[from->current].directions[DOWN] == 0);
+            if (angle > PI/2 || angle < -5*PI/6)
+                direction = LEFT;
+            else if (angle < -PI/6)
+                direction = UP;
+            else
+                direction = RIGHT;
+        }
+    } else
         return NULL;
 
     /*
@@ -1288,10 +1358,6 @@ struct bbox {
     float l, r, u, d;
 };
 
-struct game_drawstate {
-    int ox, oy;                        /* pixel position of float origin */
-};
-
 static void find_bbox_callback(void *ctx, struct grid_square *sq)
 {
     struct bbox *bb = (struct bbox *)ctx;
diff --git a/fifteen.c b/fifteen.c
index e7a41ef..49a3118 100644
--- a/fifteen.c
+++ b/fifteen.c
@@ -450,9 +450,8 @@ static void free_ui(game_ui *ui)
 {
 }
 
-static game_state *make_move(game_state *from, game_ui *ui,
-			     int x, int y, int button)
-{
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button) {
     int gx, gy, dx, dy, ux, uy, up, p;
     game_state *ret;
 
diff --git a/midend.c b/midend.c
index de20e14..1def041 100644
--- a/midend.c
+++ b/midend.c
@@ -325,7 +325,7 @@ static int midend_really_process_key(midend_data *me, int x, int y, int button)
     } else {
         game_state *s =
             me->ourgame->make_move(me->states[me->statepos-1].state,
-                                   me->ui, x, y, button);
+                                   me->ui, me->drawstate, x, y, button);
 
         if (s == me->states[me->statepos-1].state) {
             /*
diff --git a/mines.c b/mines.c
index 10ca76c..4006294 100644
--- a/mines.c
+++ b/mines.c
@@ -2229,8 +2229,8 @@ static void free_ui(game_ui *ui)
     sfree(ui);
 }
 
-static game_state *make_move(game_state *from, game_ui *ui, int x, int y,
-			     int button)
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button)
 {
     game_state *ret;
     int cx, cy;
diff --git a/net.c b/net.c
index a2204c0..447f4e3 100644
--- a/net.c
+++ b/net.c
@@ -1798,8 +1798,7 @@ static void free_ui(game_ui *ui)
  * Process a move.
  */
 static game_state *make_move(game_state *state, game_ui *ui,
-			     int x, int y, int button)
-{
+                             game_drawstate *ds, int x, int y, int button) {
     game_state *ret, *nullret;
     int tx, ty, orig;
     int shift = button & MOD_SHFT, ctrl = button & MOD_CTRL;
diff --git a/netslide.c b/netslide.c
index 324946e..b81a816 100644
--- a/netslide.c
+++ b/netslide.c
@@ -1051,7 +1051,7 @@ static void slide_col(game_state *state, int dir, int col)
 }
 
 static game_state *make_move(game_state *state, game_ui *ui,
-			     int x, int y, int button)
+                             game_drawstate *ds, int x, int y, int button)
 {
     int cx, cy;
     int n, dx, dy;
diff --git a/nullgame.c b/nullgame.c
index 3ec6b75..56694de 100644
--- a/nullgame.c
+++ b/nullgame.c
@@ -142,8 +142,8 @@ static void free_ui(game_ui *ui)
 {
 }
 
-static game_state *make_move(game_state *from, game_ui *ui, int x, int y,
-			     int button)
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button)
 {
     return NULL;
 }
diff --git a/pattern.c b/pattern.c
index 419e4aa..4cd3669 100644
--- a/pattern.c
+++ b/pattern.c
@@ -764,9 +764,8 @@ static void free_ui(game_ui *ui)
     sfree(ui);
 }
 
-static game_state *make_move(game_state *from, game_ui *ui,
-			     int x, int y, int button)
-{
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button) {
     game_state *ret;
 
     button &= ~MOD_MASK;
diff --git a/puzzles.h b/puzzles.h
index bf441c6..de0f819 100644
--- a/puzzles.h
+++ b/puzzles.h
@@ -227,8 +227,8 @@ struct game {
     char *(*text_format)(game_state *state);
     game_ui *(*new_ui)(game_state *state);
     void (*free_ui)(game_ui *ui);
-    game_state *(*make_move)(game_state *from, game_ui *ui, int x, int y,
-			     int button);
+    game_state *(*make_move)(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button);
     void (*size)(game_params *params, int *x, int *y);
     float *(*colours)(frontend *fe, game_state *state, int *ncolours);
     game_drawstate *(*new_drawstate)(game_state *state);
diff --git a/rect.c b/rect.c
index c1eaa2c..9e4204d 100644
--- a/rect.c
+++ b/rect.c
@@ -2178,9 +2178,8 @@ static void ui_draw_rect(game_state *state, game_ui *ui,
             }
 }
 
-static game_state *make_move(game_state *from, game_ui *ui,
-			     int x, int y, int button)
-{
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button) {
     int xc, yc;
     int startdrag = FALSE, enddrag = FALSE, active = FALSE;
     game_state *ret;
diff --git a/sixteen.c b/sixteen.c
index c6664c1..c202de1 100644
--- a/sixteen.c
+++ b/sixteen.c
@@ -577,9 +577,8 @@ static void free_ui(game_ui *ui)
 {
 }
 
-static game_state *make_move(game_state *from, game_ui *ui,
-			     int x, int y, int button)
-{
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button) {
     int cx, cy;
     int dx, dy, tx, ty, n;
     game_state *ret;
diff --git a/solo.c b/solo.c
index 168551c..f3afb02 100644
--- a/solo.c
+++ b/solo.c
@@ -1821,8 +1821,8 @@ static void free_ui(game_ui *ui)
     sfree(ui);
 }
 
-static game_state *make_move(game_state *from, game_ui *ui, int x, int y,
-			     int button)
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button)
 {
     int c = from->c, r = from->r, cr = c*r;
     int tx, ty;
diff --git a/twiddle.c b/twiddle.c
index f7bfd4a..273ce8c 100644
--- a/twiddle.c
+++ b/twiddle.c
@@ -618,8 +618,8 @@ static void free_ui(game_ui *ui)
 {
 }
 
-static game_state *make_move(game_state *from, game_ui *ui, int x, int y,
-			     int button)
+static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
+                             int x, int y, int button)
 {
     int w = from->w, h = from->h, n = from->n, wh = w*h;
     game_state *ret;