diff --git a/fj-app/src/camera.rs b/fj-app/src/camera.rs
index 069a5cf86..63246471d 100644
--- a/fj-app/src/camera.rs
+++ b/fj-app/src/camera.rs
@@ -1,7 +1,7 @@
 use std::f64::consts::FRAC_PI_2;
 
 use fj_interop::mesh::Mesh;
-use fj_math::{Aabb, Scalar};
+use fj_math::{Aabb, Scalar, Triangle};
 use nalgebra::{Point, TAffine, Transform, Translation, Vector};
 use parry3d_f64::query::{Ray, RayCast as _};
 use winit::dpi::PhysicalPosition;
@@ -148,11 +148,9 @@ impl Camera {
         let mut min_t = None;
 
         for triangle in mesh.triangles() {
-            let t = triangle.inner.to_parry().cast_local_ray(
-                &ray,
-                f64::INFINITY,
-                true,
-            );
+            let t = Triangle::from_points(triangle.points)
+                .to_parry()
+                .cast_local_ray(&ray, f64::INFINITY, true);
 
             if let Some(t) = t {
                 if t <= min_t.unwrap_or(t) {
diff --git a/fj-app/src/graphics/vertices.rs b/fj-app/src/graphics/vertices.rs
index 43a2c8610..ad9c2d0f8 100644
--- a/fj-app/src/graphics/vertices.rs
+++ b/fj-app/src/graphics/vertices.rs
@@ -71,7 +71,7 @@ impl From<&Mesh<fj_math::Point<3>>> for Vertices {
         let mut m = Mesh::new();
 
         for triangle in mesh.triangles() {
-            let [a, b, c] = triangle.inner.points();
+            let [a, b, c] = triangle.points;
 
             let normal = (b - a).cross(&(c - a)).normalize();
             let color = triangle.color;
diff --git a/fj-interop/src/mesh.rs b/fj-interop/src/mesh.rs
index b65874fa9..e92ab4a79 100644
--- a/fj-interop/src/mesh.rs
+++ b/fj-interop/src/mesh.rs
@@ -36,16 +36,14 @@ where
 
     /// Determine whether the mesh contains the provided triangle
     ///
-    /// Returns true, if a triangle with any combination of the points of the
-    /// provided triangle is part of the mesh.
-    pub fn contains_triangle(
-        &self,
-        triangle: impl Into<fj_math::Triangle<3>>,
-    ) -> bool {
-        let triangle = triangle.into().normalize();
+    /// Returns true, if a triangle with any combination of the provided points
+    /// is part of the mesh.
+    pub fn contains_triangle(&self, points: [impl Into<Point<3>>; 3]) -> bool {
+        let triangle = fj_math::Triangle::from_points(points).normalize();
 
         for t in &self.triangles {
-            if triangle == t.inner.normalize() {
+            let t = fj_math::Triangle::from_points(t.points).normalize();
+            if triangle == t {
                 return true;
             }
         }
@@ -71,18 +69,12 @@ where
 
 impl Mesh<Point<3>> {
     /// Add a triangle to the mesh
-    pub fn push_triangle(
-        &mut self,
-        triangle: impl Into<fj_math::Triangle<3>>,
-        color: Color,
-    ) {
-        let triangle = triangle.into();
-
-        for point in triangle.points() {
+    pub fn push_triangle(&mut self, points: [Point<3>; 3], color: Color) {
+        for point in points {
             self.push_vertex(point);
         }
 
-        self.triangles.push(Triangle::new(triangle, color));
+        self.triangles.push(Triangle { points, color });
     }
 }
 
@@ -107,20 +99,12 @@ pub type Index = u32;
 /// Extension of [`fj_math::Triangle`] that also includes a color.
 #[derive(Clone, Copy, Debug, Eq, PartialEq, Ord, PartialOrd)]
 pub struct Triangle {
-    /// The non-color part of the triangle
-    pub inner: fj_math::Triangle<3>,
+    /// The points of the triangle
+    pub points: [Point<3>; 3],
 
     /// The color of the triangle
     pub color: Color,
 }
 
-impl Triangle {
-    /// Construct a new instance of `Triangle`
-    pub fn new(inner: impl Into<fj_math::Triangle<3>>, color: Color) -> Self {
-        let inner = inner.into();
-        Self { inner, color }
-    }
-}
-
 /// RGBA color
 pub type Color = [u8; 4];
diff --git a/fj-kernel/src/algorithms/triangulation/mod.rs b/fj-kernel/src/algorithms/triangulation/mod.rs
index dba7a53b7..b388561c0 100644
--- a/fj-kernel/src/algorithms/triangulation/mod.rs
+++ b/fj-kernel/src/algorithms/triangulation/mod.rs
@@ -69,7 +69,7 @@ pub fn triangulate(
             }
             Face::Triangles(triangles) => {
                 for &(triangle, color) in triangles {
-                    mesh.push_triangle(triangle, color);
+                    mesh.push_triangle(triangle.points(), color);
                 }
             }
         }