diff --git a/Cargo.toml b/Cargo.toml
index 76b9c4b..df641c2 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,7 +1,7 @@
 [package]
 name = "myelin-geometry"
 description = "Basic linear and vector geometry for two-dimensional Euclidean geometry"
-version = "2.4.1"
+version = "2.4.2"
 authors = [
     "Jan Nils Ferner <jan@myelin.ch>",
     "Mathias Fischler <mathias@myelin.ch>",
diff --git a/changelog.md b/changelog.md
index 0325e9d..9ca0bfd 100644
--- a/changelog.md
+++ b/changelog.md
@@ -28,3 +28,6 @@
 - Correct small typos in the documentation.
 - Remove an unnecessary check.
 - Remove direct dependency on `serde_derive`.
+
+## 2.4.2
+- Explicitly disallow NaN, +∞ and -∞ in polygons instead of looping forever (#36).
diff --git a/src/polygon.rs b/src/polygon.rs
index 4147be8..3588615 100644
--- a/src/polygon.rs
+++ b/src/polygon.rs
@@ -35,7 +35,9 @@ impl Polygon {
     pub fn try_new(vertices: Vec<Point>) -> Result<Self, ()> {
         const MINIMUM_VERTICES_IN_EUCLIDEAN_GEOMETRY: usize = 3;
 
-        if vertices.len() >= MINIMUM_VERTICES_IN_EUCLIDEAN_GEOMETRY && is_convex_polygon(&vertices)
+        if vertices.len() >= MINIMUM_VERTICES_IN_EUCLIDEAN_GEOMETRY
+            && vertices.iter().all(is_finite)
+            && is_convex_polygon(&vertices)
         {
             Ok(Self { vertices })
         } else {
@@ -244,6 +246,10 @@ fn is_convex_polygon(vertices: &[Point]) -> bool {
     convex_hull_vertice_count == vertices.len()
 }
 
+fn is_finite(vertice: &Point) -> bool {
+    vertice.x.is_finite() && vertice.y.is_finite()
+}
+
 /// The side that a [`Point`] lies on, from the
 /// point of view of a line
 #[derive(Eq, PartialEq, Debug)]
@@ -561,6 +567,84 @@ mod tests {
         );
     }
 
+    #[test]
+    fn try_new_does_not_work_when_x_value_of_vertice_is_positive_infinity() {
+        let vertices = vec![
+            Point {
+                x: f64::INFINITY,
+                y: 0.0,
+            },
+            Point { x: 1.0, y: 0.0 },
+            Point { x: 0.0, y: 1.0 },
+        ];
+        assert!(Polygon::try_new(vertices).is_err());
+    }
+
+    #[test]
+    fn try_new_does_not_work_when_x_value_of_vertice_is_negative_infinity() {
+        let vertices = vec![
+            Point {
+                x: f64::NEG_INFINITY,
+                y: 0.0,
+            },
+            Point { x: 1.0, y: 0.0 },
+            Point { x: 0.0, y: 1.0 },
+        ];
+        assert!(Polygon::try_new(vertices).is_err());
+    }
+
+    #[test]
+    fn try_new_does_not_work_when_x_value_of_vertice_is_nan() {
+        let vertices = vec![
+            Point {
+                x: f64::NAN,
+                y: 0.0,
+            },
+            Point { x: 1.0, y: 0.0 },
+            Point { x: 0.0, y: 1.0 },
+        ];
+        assert!(Polygon::try_new(vertices).is_err());
+    }
+
+    #[test]
+    fn try_new_does_not_work_when_y_value_of_vertice_is_positive_infinity() {
+        let vertices = vec![
+            Point {
+                x: 0.0,
+                y: f64::INFINITY,
+            },
+            Point { x: 1.0, y: 0.0 },
+            Point { x: 0.0, y: 1.0 },
+        ];
+        assert!(Polygon::try_new(vertices).is_err());
+    }
+
+    #[test]
+    fn try_new_does_not_work_when_y_value_of_vertice_is_negative_infinity() {
+        let vertices = vec![
+            Point {
+                x: 0.0,
+                y: f64::NEG_INFINITY,
+            },
+            Point { x: 1.0, y: 0.0 },
+            Point { x: 0.0, y: 1.0 },
+        ];
+        assert!(Polygon::try_new(vertices).is_err());
+    }
+
+    #[test]
+    fn try_new_does_not_work_when_y_value_of_vertice_is_nan() {
+        let vertices = vec![
+            Point {
+                x: 0.0,
+                y: f64::NAN,
+            },
+            Point { x: 1.0, y: 0.0 },
+            Point { x: 0.0, y: 1.0 },
+        ];
+        assert!(Polygon::try_new(vertices).is_err());
+    }
+
     #[test]
     fn can_be_created_from_aabb() {
         let aabb = Aabb::try_new(Point { x: 10.0, y: 15.0 }, Point { x: 20.0, y: 30.0 }).unwrap();