diff --git a/crates/fj-kernel/src/algorithms/approx/edges.rs b/crates/fj-kernel/src/algorithms/approx/edges.rs
index 074cd947c..b24237e64 100644
--- a/crates/fj-kernel/src/algorithms/approx/edges.rs
+++ b/crates/fj-kernel/src/algorithms/approx/edges.rs
@@ -13,7 +13,7 @@ pub fn approx_edge(
     // the same vertex would be understood to refer to very close, but distinct
     // vertices.
     let vertices = vertices.convert(|vertex| {
-        geometry::Point::new(*vertex.local(), vertex.canonical().point)
+        geometry::Point::new(*vertex.local(), vertex.canonical().position())
     });
     if let Some([a, b]) = vertices {
         points.insert(0, a);
@@ -36,7 +36,7 @@ mod test {
 
     use crate::{
         geometry,
-        objects::{Vertex, VerticesOfEdge},
+        objects::{GlobalVertex, VerticesOfEdge},
         shape::LocalForm,
     };
 
@@ -47,8 +47,8 @@ mod test {
         let c = Point::from([3., 5., 8.]);
         let d = Point::from([5., 8., 13.]);
 
-        let v1 = Vertex::from_point(a);
-        let v2 = Vertex::from_point(d);
+        let v1 = GlobalVertex::from_position(a);
+        let v2 = GlobalVertex::from_position(d);
 
         let vertices = VerticesOfEdge::from_vertices([
             LocalForm::new(Point::from([0.]), v1),
diff --git a/crates/fj-kernel/src/algorithms/sweep.rs b/crates/fj-kernel/src/algorithms/sweep.rs
index f14d2f29e..34f1b4a78 100644
--- a/crates/fj-kernel/src/algorithms/sweep.rs
+++ b/crates/fj-kernel/src/algorithms/sweep.rs
@@ -2,7 +2,9 @@ use fj_math::{Point, Scalar, Transform, Triangle, Vector};
 
 use crate::{
     iter::ObjectIters,
-    objects::{Curve, Cycle, Edge, Face, Surface, Vertex, VerticesOfEdge},
+    objects::{
+        Curve, Cycle, Edge, Face, GlobalVertex, Surface, VerticesOfEdge,
+    },
     shape::LocalForm,
 };
 
@@ -87,14 +89,14 @@ fn create_top_face(
 fn create_non_continuous_side_face(
     path: Vector<3>,
     is_sweep_along_negative_direction: bool,
-    vertices_bottom: [Vertex; 2],
+    vertices_bottom: [GlobalVertex; 2],
     color: [u8; 4],
     target: &mut Vec<Face>,
 ) {
     let vertices = {
         let vertices_top = vertices_bottom.map(|vertex| {
-            let point = vertex.point + path;
-            Vertex { point }
+            let position = vertex.position() + path;
+            GlobalVertex::from_position(position)
         });
 
         let [[a, b], [c, d]] = [vertices_bottom, vertices_top];
@@ -107,7 +109,7 @@ fn create_non_continuous_side_face(
     };
 
     let surface = {
-        let [a, b, _, c] = vertices.map(|vertex| vertex.point);
+        let [a, b, _, c] = vertices.map(|vertex| vertex.position());
         Surface::plane_from_points([a, b, c])
     };
 
@@ -131,7 +133,7 @@ fn create_non_continuous_side_face(
             let curve = {
                 let local = Curve::line_from_points([a.0, b.0]);
 
-                let global = [a, b].map(|vertex| vertex.1.point);
+                let global = [a, b].map(|vertex| vertex.1.position());
                 let global = Curve::line_from_points(global);
 
                 LocalForm::new(local, global)
diff --git a/crates/fj-kernel/src/algorithms/transform.rs b/crates/fj-kernel/src/algorithms/transform.rs
index cb2916d02..57e8cdd40 100644
--- a/crates/fj-kernel/src/algorithms/transform.rs
+++ b/crates/fj-kernel/src/algorithms/transform.rs
@@ -1,7 +1,7 @@
 use fj_math::Transform;
 
 use crate::{
-    objects::{Cycle, CyclesInFace, Edge, Face, FaceBRep, Vertex},
+    objects::{Cycle, CyclesInFace, Edge, Face, FaceBRep, GlobalVertex},
     shape::LocalForm,
 };
 
@@ -58,11 +58,11 @@ pub fn transform_cycles(
 
                 let vertices =
                     edge.canonical().clone().vertices.map(|vertex| {
-                        let point = vertex.canonical().point;
-                        let point = transform.transform_point(&point);
+                        let position = vertex.canonical().position();
+                        let position = transform.transform_point(&position);
 
                         let local = *vertex.local();
-                        let canonical = Vertex { point };
+                        let canonical = GlobalVertex::from_position(position);
 
                         LocalForm::new(local, canonical)
                     });
@@ -91,11 +91,11 @@ pub fn transform_cycles(
                     LocalForm::canonical_only(curve)
                 };
                 let vertices = edge.vertices.clone().map(|vertex| {
-                    let point = vertex.canonical().point;
-                    let point = transform.transform_point(&point);
+                    let position = vertex.canonical().position();
+                    let position = transform.transform_point(&position);
 
                     let local = *vertex.local();
-                    let canonical = Vertex { point };
+                    let canonical = GlobalVertex::from_position(position);
 
                     LocalForm::new(local, canonical)
                 });
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index 8f76769a2..0e5177a77 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -2,7 +2,7 @@
 
 use std::collections::VecDeque;
 
-use crate::objects::{Curve, Cycle, Edge, Face, Surface, Vertex};
+use crate::objects::{Curve, Cycle, Edge, Face, GlobalVertex, Surface};
 
 /// Access iterators over all objects of a shape, or part of it
 ///
@@ -25,7 +25,7 @@ pub trait ObjectIters {
     fn surface_iter(&self) -> Iter<Surface>;
 
     /// Iterate over all vertices
-    fn vertex_iter(&self) -> Iter<Vertex>;
+    fn vertex_iter(&self) -> Iter<GlobalVertex>;
 }
 
 impl ObjectIters for Curve<3> {
@@ -49,7 +49,7 @@ impl ObjectIters for Curve<3> {
         Iter::empty()
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         Iter::empty()
     }
 }
@@ -99,7 +99,7 @@ impl ObjectIters for Cycle<3> {
         iter
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         let mut iter = Iter::empty();
 
         for edge in self.edges() {
@@ -155,7 +155,7 @@ impl ObjectIters for Edge<3> {
         iter
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         let mut iter = Iter::empty().with(self.curve().vertex_iter());
 
         for vertex in self.vertices().into_iter().flatten() {
@@ -227,7 +227,7 @@ impl ObjectIters for Face {
         Iter::empty()
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         if let Face::Face(face) = self {
             let mut iter = Iter::empty().with(face.surface().vertex_iter());
 
@@ -263,12 +263,12 @@ impl ObjectIters for Surface {
         Iter::from_object(*self)
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         Iter::empty()
     }
 }
 
-impl ObjectIters for Vertex {
+impl ObjectIters for GlobalVertex {
     fn curve_iter(&self) -> Iter<Curve<3>> {
         Iter::empty()
     }
@@ -289,7 +289,7 @@ impl ObjectIters for Vertex {
         Iter::empty()
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         Iter::from_object(*self)
     }
 }
@@ -354,7 +354,7 @@ where
         iter
     }
 
-    fn vertex_iter(&self) -> Iter<Vertex> {
+    fn vertex_iter(&self) -> Iter<GlobalVertex> {
         let mut iter = Iter::empty();
 
         for face in self.into_iter() {
@@ -405,7 +405,7 @@ impl<T> Iterator for Iter<T> {
 
 #[cfg(test)]
 mod tests {
-    use crate::objects::{Curve, Cycle, Edge, Face, Surface, Vertex};
+    use crate::objects::{Curve, Cycle, Edge, Face, GlobalVertex, Surface};
 
     use super::ObjectIters as _;
 
@@ -478,7 +478,7 @@ mod tests {
 
     #[test]
     fn vertex() {
-        let vertex = Vertex::from_point([0., 0., 0.]);
+        let vertex = GlobalVertex::from_position([0., 0., 0.]);
 
         assert_eq!(0, vertex.curve_iter().count());
         assert_eq!(0, vertex.cycle_iter().count());
diff --git a/crates/fj-kernel/src/objects/edge.rs b/crates/fj-kernel/src/objects/edge.rs
index 8d8e79892..490ab709e 100644
--- a/crates/fj-kernel/src/objects/edge.rs
+++ b/crates/fj-kernel/src/objects/edge.rs
@@ -4,7 +4,7 @@ use fj_math::{Circle, Line, Point, Scalar, Vector};
 
 use crate::shape::LocalForm;
 
-use super::{Curve, Vertex};
+use super::{Curve, GlobalVertex};
 
 /// An edge of a shape
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
@@ -36,7 +36,7 @@ impl<const D: usize> Edge<D> {
     ///
     /// This is a convenience method that saves the caller from dealing with the
     /// [`Handle`]s.
-    pub fn vertices(&self) -> Option<[Vertex; 2]> {
+    pub fn vertices(&self) -> Option<[GlobalVertex; 2]> {
         self.vertices
             .0
             .as_ref()
@@ -76,18 +76,18 @@ impl Edge<3> {
     pub fn line_segment_from_points(
         vertices: [impl Into<Point<3>>; 2],
     ) -> Self {
-        let vertices = vertices.map(|point| {
-            let point = point.into();
-            Vertex { point }
+        let vertices = vertices.map(|position| {
+            let position = position.into();
+            GlobalVertex::from_position(position)
         });
 
         Self::line_segment_from_vertices(vertices)
     }
 
     /// Create a line segment from two vertices
-    pub fn line_segment_from_vertices([a, b]: [Vertex; 2]) -> Self {
+    pub fn line_segment_from_vertices([a, b]: [GlobalVertex; 2]) -> Self {
         let curve = {
-            let points = [a, b].map(|vertex| vertex.point);
+            let points = [a, b].map(|vertex| vertex.position());
             Curve::Line(Line::from_points(points))
         };
 
@@ -107,7 +107,7 @@ impl<const D: usize> fmt::Display for Edge<D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         match self.vertices() {
             Some(vertices) => {
-                let [a, b] = vertices.map(|vertex| vertex.point);
+                let [a, b] = vertices.map(|vertex| vertex.position());
                 write!(f, "edge from {:?} to {:?}", a, b)?
             }
             None => write!(f, "continuous edge")?,
@@ -121,16 +121,20 @@ impl<const D: usize> fmt::Display for Edge<D> {
 
 /// The vertices that bound an edge
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
-pub struct VerticesOfEdge(Option<[LocalForm<Point<1>, Vertex>; 2]>);
+pub struct VerticesOfEdge(Option<[LocalForm<Point<1>, GlobalVertex>; 2]>);
 
 impl VerticesOfEdge {
     /// Construct an instance of `VerticesOfEdge` from zero or two vertices
-    pub fn new(vertices: Option<[LocalForm<Point<1>, Vertex>; 2]>) -> Self {
+    pub fn new(
+        vertices: Option<[LocalForm<Point<1>, GlobalVertex>; 2]>,
+    ) -> Self {
         Self(vertices)
     }
 
     /// Construct an instance of `VerticesOfEdge` from two vertices
-    pub fn from_vertices(vertices: [LocalForm<Point<1>, Vertex>; 2]) -> Self {
+    pub fn from_vertices(
+        vertices: [LocalForm<Point<1>, GlobalVertex>; 2],
+    ) -> Self {
         Self(Some(vertices))
     }
 
@@ -164,12 +168,14 @@ impl VerticesOfEdge {
     /// # Panics
     ///
     /// Panics, if the edge has no vertices.
-    pub fn expect_vertices(self) -> [LocalForm<Point<1>, Vertex>; 2] {
+    pub fn expect_vertices(self) -> [LocalForm<Point<1>, GlobalVertex>; 2] {
         self.0.expect("Expected edge to have vertices")
     }
 
     /// Iterate over the vertices, if any
-    pub fn iter(&self) -> impl Iterator<Item = &LocalForm<Point<1>, Vertex>> {
+    pub fn iter(
+        &self,
+    ) -> impl Iterator<Item = &LocalForm<Point<1>, GlobalVertex>> {
         self.0.iter().flatten()
     }
 
@@ -188,7 +194,9 @@ impl VerticesOfEdge {
     /// Map each vertex using the provided function
     pub fn map<F>(self, f: F) -> Self
     where
-        F: FnMut(LocalForm<Point<1>, Vertex>) -> LocalForm<Point<1>, Vertex>,
+        F: FnMut(
+            LocalForm<Point<1>, GlobalVertex>,
+        ) -> LocalForm<Point<1>, GlobalVertex>,
     {
         Self(self.convert(f))
     }
@@ -196,7 +204,7 @@ impl VerticesOfEdge {
     /// Convert each vertex using the provided function
     pub fn convert<F, T>(self, f: F) -> Option<[T; 2]>
     where
-        F: FnMut(LocalForm<Point<1>, Vertex>) -> T,
+        F: FnMut(LocalForm<Point<1>, GlobalVertex>) -> T,
     {
         self.0.map(|vertices| vertices.map(f))
     }
@@ -204,7 +212,7 @@ impl VerticesOfEdge {
     /// Convert each vertex using the provided fallible function
     pub fn try_convert<F, T, E>(self, f: F) -> Result<Option<[T; 2]>, E>
     where
-        F: FnMut(LocalForm<Point<1>, Vertex>) -> Result<T, E>,
+        F: FnMut(LocalForm<Point<1>, GlobalVertex>) -> Result<T, E>,
     {
         // Can be cleaned up using `try_map`, once that is stable:
         // https://doc.rust-lang.org/std/primitive.array.html#method.try_map
diff --git a/crates/fj-kernel/src/objects/vertex.rs b/crates/fj-kernel/src/objects/global_vertex.rs
similarity index 74%
rename from crates/fj-kernel/src/objects/vertex.rs
rename to crates/fj-kernel/src/objects/global_vertex.rs
index 9252c8e69..d3447455d 100644
--- a/crates/fj-kernel/src/objects/vertex.rs
+++ b/crates/fj-kernel/src/objects/global_vertex.rs
@@ -19,15 +19,19 @@ use fj_math::Point;
 /// between distinct vertices can be configured using
 /// [`Shape::with_minimum_distance`].
 #[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
-pub struct Vertex {
-    /// The point that defines the location of the vertex
-    pub point: Point<3>,
+pub struct GlobalVertex {
+    position: Point<3>,
 }
 
-impl Vertex {
+impl GlobalVertex {
     /// Construct a `Vertex` from a point
-    pub fn from_point(point: impl Into<Point<3>>) -> Self {
-        let point = point.into();
-        Self { point }
+    pub fn from_position(position: impl Into<Point<3>>) -> Self {
+        let position = position.into();
+        Self { position }
+    }
+
+    /// The position of the vertex
+    pub fn position(&self) -> Point<3> {
+        self.position
     }
 }
diff --git a/crates/fj-kernel/src/objects/mod.rs b/crates/fj-kernel/src/objects/mod.rs
index 7f05c7904..8ecfb7665 100644
--- a/crates/fj-kernel/src/objects/mod.rs
+++ b/crates/fj-kernel/src/objects/mod.rs
@@ -8,14 +8,14 @@ mod curve;
 mod cycle;
 mod edge;
 mod face;
+mod global_vertex;
 mod surface;
-mod vertex;
 
 pub use self::{
     curve::Curve,
     cycle::Cycle,
     edge::{Edge, VerticesOfEdge},
     face::{CyclesInFace, Face, FaceBRep},
+    global_vertex::GlobalVertex,
     surface::{Surface, SweptCurve},
-    vertex::Vertex,
 };
diff --git a/crates/fj-kernel/src/validation/coherence.rs b/crates/fj-kernel/src/validation/coherence.rs
index 10d9ecb52..f5f2b7ccd 100644
--- a/crates/fj-kernel/src/validation/coherence.rs
+++ b/crates/fj-kernel/src/validation/coherence.rs
@@ -19,7 +19,7 @@ pub fn validate_edge(
     for vertex in edge.vertices.iter() {
         let local = *vertex.local();
         let local_as_canonical = edge.curve().point_from_curve_coords(local);
-        let canonical = vertex.canonical().point;
+        let canonical = vertex.canonical().position();
         let distance = (local_as_canonical - canonical).magnitude();
 
         if distance > max_distance {
diff --git a/crates/fj-kernel/src/validation/mod.rs b/crates/fj-kernel/src/validation/mod.rs
index 484adccc6..eaafc96f5 100644
--- a/crates/fj-kernel/src/validation/mod.rs
+++ b/crates/fj-kernel/src/validation/mod.rs
@@ -141,7 +141,7 @@ mod tests {
     use fj_math::{Point, Scalar};
 
     use crate::{
-        objects::{Curve, Edge, Vertex, VerticesOfEdge},
+        objects::{Curve, Edge, GlobalVertex, VerticesOfEdge},
         shape::LocalForm,
         validation::{validate, ValidationConfig, ValidationError},
     };
@@ -156,8 +156,8 @@ mod tests {
             LocalForm::canonical_only(curve)
         };
 
-        let a = Vertex { point: a };
-        let b = Vertex { point: b };
+        let a = GlobalVertex::from_position(a);
+        let b = GlobalVertex::from_position(b);
 
         let deviation = Scalar::from_f64(0.25);
 
@@ -203,11 +203,11 @@ mod tests {
         };
 
         // Adding a vertex should work.
-        shape.push(Vertex { point: a });
+        shape.push(GlobalVertex::from_position(a));
         validate(shape.clone(), &config)?;
 
         // Adding a second vertex that is considered identical should fail.
-        shape.push(Vertex { point: b });
+        shape.push(GlobalVertex::from_position(b));
         let result = validate(shape, &config);
         assert!(matches!(result, Err(ValidationError::Uniqueness(_))));
 
diff --git a/crates/fj-kernel/src/validation/uniqueness.rs b/crates/fj-kernel/src/validation/uniqueness.rs
index 311e21e1b..516740d81 100644
--- a/crates/fj-kernel/src/validation/uniqueness.rs
+++ b/crates/fj-kernel/src/validation/uniqueness.rs
@@ -2,15 +2,16 @@ use std::{collections::HashSet, fmt};
 
 use fj_math::Scalar;
 
-use crate::objects::Vertex;
+use crate::objects::GlobalVertex;
 
 pub fn validate_vertex(
-    vertex: &Vertex,
-    vertices: &HashSet<Vertex>,
+    vertex: &GlobalVertex,
+    vertices: &HashSet<GlobalVertex>,
     min_distance: Scalar,
 ) -> Result<(), UniquenessIssues> {
     for existing in vertices {
-        if (existing.point - vertex.point).magnitude() < min_distance {
+        if (existing.position() - vertex.position()).magnitude() < min_distance
+        {
             return Err(UniquenessIssues {
                 duplicate_vertex: Some(*existing),
             });
@@ -34,7 +35,7 @@ pub fn validate_vertex(
 #[derive(Debug, Default, thiserror::Error)]
 pub struct UniquenessIssues {
     /// Duplicate vertex found
-    pub duplicate_vertex: Option<Vertex>,
+    pub duplicate_vertex: Option<GlobalVertex>,
 }
 
 impl fmt::Display for UniquenessIssues {