diff --git a/package/MDAnalysis/core/groups.py b/package/MDAnalysis/core/groups.py
index 70d826d7675..f50aeca1e18 100644
--- a/package/MDAnalysis/core/groups.py
+++ b/package/MDAnalysis/core/groups.py
@@ -3111,14 +3111,13 @@ def select_atoms(self, sel, *othersel, periodic=True, rtol=1e-05,
                 radius 5, external radius 10 centered on the COG. In z, the
                 cylinder extends from 10 above the COG to 8 below. Positive
                 values for *zMin*, or negative ones for *zMax*, are allowed.
-            box *dimensions* *dN_min* *dN_max* *selection*
+            box *dimensions* *dN_min* *dN_max* [*dN_min* *dN_max*] [*dN_min* *dN_max*] *selection*
                 Select all atoms within a box region centered
                 on the center of geometry (COG) of a given selection.
                 *dimensions* Specifies which dimension(s) to apply
-                the box selection on. Can be ``x``, ``y``, ``z``,
-                or any combination like ``xy``, ``yz``, ``zx``, ``xyz``
-                (up to 3 characters). *dN_min*, *dN_max* are the minimum and
-                maximum bounds along the first specified dimension.
+                the box selection on. Can be ``x``, ``y``, ``z``, ``xy``, 
+                ``yz``, ``xz``, or ``xyz`. *dN_min*, *dN_max* are the minimum 
+                and maximum bounds along each specified dimension.
                 Positive values are above/right/front of the COG,
                 negatives are below/left/behind, and should be specified
                 for each dimension. *selection* specifies the selection
diff --git a/package/MDAnalysis/core/selection.py b/package/MDAnalysis/core/selection.py
index 6813a2216fd..d66a304b246 100644
--- a/package/MDAnalysis/core/selection.py
+++ b/package/MDAnalysis/core/selection.py
@@ -540,24 +540,8 @@ def _apply(self, group):
 class BoxSelection(Selection):
     token = "box"
     precedence = 1
-    combination = [
-        "x",
-        "y",
-        "z",
-        "xy",
-        "xz",
-        "yz",
-        "yx",
-        "zx",
-        "zy",
-        "xyz",
-        "xzy",
-        "yxz",
-        "yzx",
-        "zxy",
-        "zyx",
-    ]
     axis_map = ["x", "y", "z"]
+    axis_set = {"x", "y", "z", "xy", "xz", "yz", "xyz"}
 
     def __init__(self, parser, tokens):
         super().__init__(parser, tokens)
@@ -566,22 +550,31 @@ def __init__(self, parser, tokens):
         self.xmin, self.xmax = None, None
         self.ymin, self.ymax = None, None
         self.zmin, self.zmax = None, None
-        if self.direction not in self.combination:
-            raise ValueError(
-                "The direction '{}' is not valid. Must be combination of {}"
-                "".format(self.direction, ["x", "y", "z"])
-            )
-        else:
+
+        if self.direction in self.axis_set:
             for d in self.direction:
                 if d == "x":
                     self.xmin = float(tokens.popleft())
                     self.xmax = float(tokens.popleft())
+                    if self.xmin > self.xmax:
+                        raise ValueError("xmin must be less than or equal to xmax")
                 elif d == "y":
                     self.ymin = float(tokens.popleft())
                     self.ymax = float(tokens.popleft())
+                    if self.ymin > self.ymax:
+                        raise ValueError("ymin must be less than or equal to ymax")
                 elif d == "z":
                     self.zmin = float(tokens.popleft())
                     self.zmax = float(tokens.popleft())
+                    if self.zmin > self.zmax:
+                        raise ValueError("zmin must be less than or equal to zmax")
+        else:
+            raise ValueError(
+                "The direction '{}' is not valid. "
+                "Must be one of {}"
+                "".format(self.direction, ", ".join(self.axis_set))
+            )
+
         self.sel = parser.parse_expression(self.precedence)
 
     @return_empty_on_apply
diff --git a/package/doc/sphinx/source/documentation_pages/selections.rst b/package/doc/sphinx/source/documentation_pages/selections.rst
index 196446bc9df..9d500e08a27 100644
--- a/package/doc/sphinx/source/documentation_pages/selections.rst
+++ b/package/doc/sphinx/source/documentation_pages/selections.rst
@@ -280,9 +280,9 @@ cyzone *externalRadius* *zMax* *zMin* *selection*
 box *dimensions* *dN_min* *dN_max* *selection*
     Select all atoms within a box region centered on the center of 
     geometry (COG) of a given selection. *dimensions* Specifies 
-    which dimension(s) to apply the box selection on. Can be ``x``, 
-    ``y``, ``z``, or any combination like ``xy``, ``yz``, ``zx``, ``xyz`` 
-    (up to 3 characters). *dN_min*, *dN_max* are the minimum and maximum 
+    which dimension(s) to apply the box selection on. 
+    Can be ``x``, ``y``, ``z``, ``xy``, ``yz``, ``xz``, or ``xyz`. 
+    *dN_min*, *dN_max* are the minimum and maximum 
     bounds along the first specified dimension. Positive values are 
     above/right/front of the COG, negatives are below/left/behind. 
     Should be specified for each dimension. *selection* specifies the selection