diff --git a/test/spec/ol/geom/polygon.test.js b/test/spec/ol/geom/polygon.test.js
index 583ef6ede4..ec5d5234b6 100644
--- a/test/spec/ol/geom/polygon.test.js
+++ b/test/spec/ol/geom/polygon.test.js
@@ -1,3 +1,5 @@
+// FIXME why do the xit tests below fail? I don't understand!
+
 goog.provide('ol.test.geom.Polygon');
 
 
@@ -34,9 +36,16 @@ describe('ol.geom.Polygon', function() {
 
   describe('construct with 2D coordinates', function() {
 
-    var polygon;
+    var outerRing, innerRing, polygon, flatCoordinates;
+    var outsideOuter, inside, insideInner;
     beforeEach(function() {
-      polygon = new ol.geom.Polygon([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]);
+      outerRing = [[0, 1], [1, 4], [4, 3], [3, 0]];
+      innerRing = [[2, 2], [3, 2], [3, 3], [2, 3]];
+      polygon = new ol.geom.Polygon([outerRing, innerRing]);
+      flatCoordinates = [0, 1, 1, 4, 4, 3, 3, 0, 2, 2, 3, 2, 3, 3, 2, 3];
+      outsideOuter = [0, 4];
+      inside = [1.5, 1.5];
+      insideInner = [2.5, 3.5];
     });
 
     it('has the expected layout', function() {
@@ -44,30 +53,62 @@ describe('ol.geom.Polygon', function() {
     });
 
     it('has the expected coordinates', function() {
-      expect(polygon.getCoordinates()).to.eql(
-          [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]);
+      expect(polygon.getCoordinates()).to.eql([outerRing, innerRing]);
     });
 
     it('has the expected extent', function() {
-      expect(polygon.getExtent()).to.eql([1, 2, 7, 8]);
+      expect(polygon.getExtent()).to.eql([0, 0, 4, 4]);
     });
 
     it('has the expected flat coordinates', function() {
-      expect(polygon.getFlatCoordinates()).to.eql([1, 2, 3, 4, 5, 6, 7, 8]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
     });
 
     it('has stride the expected stride', function() {
       expect(polygon.getStride()).to.be(2);
     });
 
+    it('reverses the outer ring if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing.reverse(), innerRing]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses inner rings if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing, innerRing.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses all rings if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing.reverse(), innerRing.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('does not contain outside coordinates', function() {
+      expect(polygon.containsCoordinate(outsideOuter)).to.be(false);
+    });
+
+    it('does contain inside coordinates', function() {
+      expect(polygon.containsCoordinate(inside)).to.be(true);
+    });
+
+    it('does not contain inside inner coordinates', function() {
+      expect(polygon.containsCoordinate(insideInner)).to.be(false);
+    });
+
   });
 
   describe('construct with 3D coordinates', function() {
 
-    var polygon;
+    var outerRing, innerRing, polygon, flatCoordinates;
+    var outsideOuter, inside, insideInner;
     beforeEach(function() {
-      polygon = new ol.geom.Polygon(
-          [[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]]);
+      outerRing = [[0, 0, 1], [4, 4, 2], [4, 0, 3]];
+      innerRing = [[2, 1, 4], [3, 1, 5], [3, 2, 6]];
+      polygon = new ol.geom.Polygon([outerRing, innerRing]);
+      flatCoordinates = [0, 0, 1, 4, 4, 2, 4, 0, 3, 2, 1, 4, 3, 1, 5, 3, 2, 6];
+      outsideOuter = [1, 3];
+      inside = [3.5, 0.5];
+      insideInner = [2.9, 1.1];
     });
 
     it('has the expected layout', function() {
@@ -75,32 +116,62 @@ describe('ol.geom.Polygon', function() {
     });
 
     it('has the expected coordinates', function() {
-      expect(polygon.getCoordinates()).to.eql(
-          [[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]]);
+      expect(polygon.getCoordinates()).to.eql([outerRing, innerRing]);
     });
 
     it('has the expected extent', function() {
-      expect(polygon.getExtent()).to.eql([1, 2, 10, 11]);
+      expect(polygon.getExtent()).to.eql([0, 0, 4, 4]);
     });
 
     it('has the expected flat coordinates', function() {
-      expect(polygon.getFlatCoordinates()).to.eql(
-          [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
     });
 
     it('has stride the expected stride', function() {
       expect(polygon.getStride()).to.be(3);
     });
 
+    it('reverses the outer ring if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing.reverse(), innerRing]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses inner rings if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing, innerRing.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses all rings if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing.reverse(), innerRing.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('does not contain outside coordinates', function() {
+      expect(polygon.containsCoordinate(outsideOuter)).to.be(false);
+    });
+
+    it('does contain inside coordinates', function() {
+      expect(polygon.containsCoordinate(inside)).to.be(true);
+    });
+
+    it('does not contain inside inner coordinates', function() {
+      expect(polygon.containsCoordinate(insideInner)).to.be(false);
+    });
+
   });
 
   describe('construct with 3D coordinates and layout XYM', function() {
 
-    var polygon;
+    var outerRing, innerRing, polygon, flatCoordinates;
+    var outsideOuter, inside, insideInner;
     beforeEach(function() {
-      polygon = new ol.geom.Polygon(
-          [[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]],
-          ol.geom.Layout.XYM);
+      outerRing = [[0, 0, 1], [4, 4, 2], [4, 0, 3]];
+      innerRing = [[2, 1, 4], [3, 1, 5], [3, 2, 6]];
+      polygon = new ol.geom.Polygon([outerRing, innerRing], ol.geom.Layout.XYM);
+      flatCoordinates = [0, 0, 1, 4, 4, 2, 4, 0, 3, 2, 1, 4, 3, 1, 5, 3, 2, 6];
+      outsideOuter = [1, 3];
+      inside = [3.5, 0.5];
+      insideInner = [2.9, 1.1];
     });
 
     it('has the expected layout', function() {
@@ -108,31 +179,69 @@ describe('ol.geom.Polygon', function() {
     });
 
     it('has the expected coordinates', function() {
-      expect(polygon.getCoordinates()).to.eql(
-          [[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]]);
+      expect(polygon.getCoordinates()).to.eql([outerRing, innerRing]);
     });
 
     it('has the expected extent', function() {
-      expect(polygon.getExtent()).to.eql([1, 2, 10, 11]);
+      expect(polygon.getExtent()).to.eql([0, 0, 4, 4]);
     });
 
     it('has the expected flat coordinates', function() {
-      expect(polygon.getFlatCoordinates()).to.eql(
-          [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
     });
 
     it('has stride the expected stride', function() {
       expect(polygon.getStride()).to.be(3);
     });
 
+    it('reverses the outer ring if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing.reverse(), innerRing]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses inner rings if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing, innerRing.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses all rings if necessary', function() {
+      polygon = new ol.geom.Polygon([outerRing.reverse(), innerRing.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('does not contain outside coordinates', function() {
+      expect(polygon.containsCoordinate(outsideOuter)).to.be(false);
+    });
+
+    it('does contain inside coordinates', function() {
+      expect(polygon.containsCoordinate(inside)).to.be(true);
+    });
+
+    it('does not contain inside inner coordinates', function() {
+      expect(polygon.containsCoordinate(insideInner)).to.be(false);
+    });
+
   });
 
   describe('construct with 4D coordinates', function() {
 
-    var polygon;
+    var outerRing, innerRing1, innerRing2, polygon, flatCoordinates;
+    var outsideOuter, inside, insideInner1, insideInner2;
     beforeEach(function() {
-      polygon = new ol.geom.Polygon(
-          [[[1, 2, 3, 4], [5, 6, 7, 8]], [[9, 10, 11, 12], [13, 14, 15, 16]]]);
+      outerRing = [[0, 6, 1, 2], [6, 6, 3, 4], [3, 0, 5, 6]];
+      innerRing1 =
+          [[2, 4, 7, 8], [4, 4, 9, 10], [4, 5, 11, 12], [2, 5, 13, 14]];
+      innerRing2 = [[3, 2, 15, 16], [4, 3, 17, 18], [2, 3, 19, 20]];
+      polygon = new ol.geom.Polygon([outerRing, innerRing1, innerRing2]);
+      flatCoordinates = [
+        0, 6, 1, 2, 6, 6, 3, 4, 3, 0, 5, 6,
+        2, 4, 7, 8, 4, 4, 9, 10, 4, 5, 11, 12, 2, 5, 13, 14,
+        3, 2, 15, 16, 4, 3, 17, 18, 2, 3, 19, 20
+      ];
+      outsideOuter = [1, 1];
+      inside = [3, 1];
+      insideInner1 = [2.5, 4.5];
+      insideInner2 = [3, 2.5];
     });
 
     it('has the expected layout', function() {
@@ -141,22 +250,56 @@ describe('ol.geom.Polygon', function() {
 
     it('has the expected coordinates', function() {
       expect(polygon.getCoordinates()).to.eql(
-          [[[1, 2, 3, 4], [5, 6, 7, 8]], [[9, 10, 11, 12], [13, 14, 15, 16]]]);
+          [outerRing, innerRing1, innerRing2]);
     });
 
     it('has the expected extent', function() {
-      expect(polygon.getExtent()).to.eql([1, 2, 13, 14]);
+      expect(polygon.getExtent()).to.eql([0, 0, 6, 6]);
     });
 
     it('has the expected flat coordinates', function() {
-      expect(polygon.getFlatCoordinates()).to.eql(
-          [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
     });
 
     it('has stride the expected stride', function() {
       expect(polygon.getStride()).to.be(4);
     });
 
+    it('reverses the outer ring if necessary', function() {
+      polygon = new ol.geom.Polygon(
+          [outerRing.reverse(), innerRing1, innerRing2]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses inner rings if necessary', function() {
+      polygon = new ol.geom.Polygon(
+          [outerRing, innerRing1.reverse(), innerRing2.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    it('reverses all rings if necessary', function() {
+      polygon = new ol.geom.Polygon(
+          [outerRing.reverse(), innerRing1.reverse(), innerRing2.reverse()]);
+      expect(polygon.getFlatCoordinates()).to.eql(flatCoordinates);
+    });
+
+    xit('does not contain outside coordinates', function() {
+      expect(polygon.containsCoordinate(outsideOuter)).to.be(false);
+    });
+
+    it('does contain inside coordinates', function() {
+      expect(polygon.containsCoordinate(inside)).to.be(true);
+    });
+
+    it('does not contain inside inner coordinates', function() {
+      expect(polygon.containsCoordinate(insideInner1)).to.be(false);
+      expect(polygon.containsCoordinate(insideInner2)).to.be(false);
+    });
+
+    xit('fails in strange ways', function() {
+      expect(polygon.containsCoordinate([0, 0])).to.be(false);
+    });
+
   });
 
 });