diff --git a/crates/fj-core/src/algorithms/approx/cycle.rs b/crates/fj-core/src/algorithms/approx/cycle.rs
index 0a17cd2ba..dfedcdf38 100644
--- a/crates/fj-core/src/algorithms/approx/cycle.rs
+++ b/crates/fj-core/src/algorithms/approx/cycle.rs
@@ -12,6 +12,7 @@ use crate::{
 
 use super::{
     half_edge::{approx_half_edge, HalfEdgeApprox},
+    vertex::approx_vertex,
     ApproxCache, ApproxPoint, Tolerance,
 };
 
@@ -30,12 +31,23 @@ pub fn approx_cycle(
         .iter()
         .map(|half_edge| {
             let boundary = geometry.of_half_edge(half_edge).boundary;
+            let [start_position_curve, _] = boundary.inner;
+
+            let start = approx_vertex(
+                half_edge.start_vertex().clone(),
+                half_edge.curve(),
+                surface,
+                start_position_curve,
+                &mut cache.vertex,
+                geometry,
+            );
+
             approx_half_edge(
                 half_edge,
                 surface,
+                start,
                 boundary,
                 tolerance,
-                &mut cache.vertex,
                 &mut cache.curve,
                 geometry,
             )
diff --git a/crates/fj-core/src/algorithms/approx/half_edge.rs b/crates/fj-core/src/algorithms/approx/half_edge.rs
index 2a847b8c0..75dab518b 100644
--- a/crates/fj-core/src/algorithms/approx/half_edge.rs
+++ b/crates/fj-core/src/algorithms/approx/half_edge.rs
@@ -14,7 +14,6 @@ use crate::{
 
 use super::{
     curve::{approx_curve_with_cache, CurveApproxCache},
-    vertex::{approx_vertex, VertexApproxCache},
     ApproxPoint, Tolerance,
 };
 
@@ -22,25 +21,14 @@ use super::{
 pub fn approx_half_edge(
     half_edge: &Handle<HalfEdge>,
     surface: &Handle<Surface>,
+    start: ApproxPoint<1>,
     boundary: CurveBoundary<Point<1>>,
     tolerance: impl Into<Tolerance>,
-    vertex_cache: &mut VertexApproxCache,
     curve_cache: &mut CurveApproxCache,
     geometry: &Geometry,
 ) -> HalfEdgeApprox {
     let tolerance = tolerance.into();
 
-    let [start_position_curve, _] = boundary.inner;
-
-    let start = approx_vertex(
-        half_edge.start_vertex().clone(),
-        half_edge.curve(),
-        surface,
-        start_position_curve,
-        vertex_cache,
-        geometry,
-    );
-
     let rest = approx_curve_with_cache(
         half_edge.curve(),
         surface,