diff --git a/genstar/Test.hs b/genstar/Test.hs
index ffa8f8f..9eca71e 100644
--- a/genstar/Test.hs
+++ b/genstar/Test.hs
@@ -2,13 +2,25 @@
 
 module Test where
 
-import Main (Vertex (Point), fromAngle, move, scale, vertexDistance)
-import Test.QuickCheck (discard, quickCheck, quickCheckAll)
+import Data.List (partition)
+import Main (PolygonPath (PolygonPath), Vertex (Point), fromAngle, move, regularPolygon, scale, star, vertexDistance)
+import Test.QuickCheck (Arbitrary (arbitrary), Positive, chooseInteger, discard, getPositive, quickCheck, quickCheckAll)
+
+newtype PolygonVertexCount a = PolygonVertexCount a deriving (Show)
+
+instance Integral a => Arbitrary (PolygonVertexCount a) where
+  arbitrary = do
+    x <- chooseInteger (3, 1000)
+    return $ PolygonVertexCount (fromIntegral x)
 
 -- | the largest acceptable difference between two doubles so they are considered equal
 epsilon :: Double
 epsilon = 1e-10
 
+getVertices :: Maybe PolygonPath -> [Vertex]
+getVertices (Just (PolygonPath ps)) = ps
+getVertices Nothing = []
+
 -- | checks whether the distance of a vertex constructed by 'fromAngle' to the origin is 1
 prop_VertexFromAngleDistance :: Double -> Bool
 prop_VertexFromAngleDistance angle = abs (1 - vertexDistance (fromAngle angle)) < epsilon
@@ -25,6 +37,25 @@ prop_MoveSelfEqualsScale2 p = move p p == scale 2 p
 prop_MoveNegativeSelfEqualsOrigin :: Vertex -> Bool
 prop_MoveNegativeSelfEqualsOrigin p = move p (scale (-1) p) == Point (0, 0)
 
+-- | checks whether distance of points of a regular polygon have the radius as distance from the origin
+prop_RegularPolygonPointsDistance :: Integral a => (PolygonVertexCount a, Positive Double) -> Bool
+prop_RegularPolygonPointsDistance (PolygonVertexCount n, r) = all (\p -> abs (vertexDistance p - getPositive r) < epsilon) (getVertices (regularPolygon (fromIntegral n) (getPositive r) (Point (0, 0))))
+
+-- | checks whether the average of all polygon points equals the specified centre point
+prop_RegularPolygonCentre :: (Integral a) => (PolygonVertexCount a, Positive Double, Vertex) -> Bool
+prop_RegularPolygonCentre (PolygonVertexCount n, r, p) = abs (specX - calcX) < epsilon && abs (specY - calcY) < epsilon
+  where
+    Point (specX, specY) = p
+    Point (calcX, calcY) = scale (1 / fromIntegral n) $ foldr move (Point (0, 0)) (getVertices (regularPolygon (fromIntegral n) (getPositive r) p))
+
+-- | checks whether the distance of all points of a star from the centre can be partitioned into two classes,
+-- both of the same size, the number of spikes
+prop_StarDistancePartitioning :: (Integral a) => (PolygonVertexCount a, Positive Double, Positive Double) -> Bool
+prop_StarDistancePartitioning (PolygonVertexCount n, r1, r2) = length c1 == length c2 && length c1 == fromIntegral n
+  where
+    (c1, c2) = partition (\x -> abs (getPositive r1 - vertexDistance x) > abs (getPositive r2 - vertexDistance x)) vertices
+    vertices = getVertices (star (fromIntegral n) (getPositive r1) (getPositive r2) (Point (0, 0)))
+
 return []
 
 check = $quickCheckAll