diff --git a/src/scene/page_setup.rs b/src/scene/page_setup.rs
index af3926e75..193264d13 100644
--- a/src/scene/page_setup.rs
+++ b/src/scene/page_setup.rs
@@ -175,7 +175,23 @@ impl Scene {
         let ObjectType::Dictionary(d) = self.document.objects.get(&dh)? else {
             return None;
         };
-        d.entries.iter().find(|(k, _)| k == name).map(|(_, h)| *h)
+        d.entries
+            .iter()
+            .find(|(k, _)| k.eq_ignore_ascii_case(name))
+            .map(|(_, h)| *h)
+    }
+
+    /// The dictionary's own spelling of `name` (page-setup names compare
+    /// case-insensitively, like every named-object dictionary key).
+    fn page_setup_key(&self, name: &str) -> Option<String> {
+        let dh = self.plotsettings_dict_handle()?;
+        let ObjectType::Dictionary(d) = self.document.objects.get(&dh)? else {
+            return None;
+        };
+        d.entries
+            .iter()
+            .find(|(k, _)| k.eq_ignore_ascii_case(name))
+            .map(|(k, _)| k.clone())
     }
 
     /// Create or update the named page setup from `ps` (its `page_name` and
@@ -183,7 +199,9 @@ impl Scene {
     /// are inserted and registered in the dictionary.
     pub fn page_setup_save(&mut self, name: &str, mut ps: PlotSettings) {
         let dict_handle = self.ensure_plotsettings_dict();
-        ps.page_name = name.to_string();
+        // Replacing keeps the entry's stored spelling so the dictionary key
+        // and the object's page_name stay one name.
+        ps.page_name = self.page_setup_key(name).unwrap_or_else(|| name.to_string());
         ps.owner = dict_handle;
         if let Some(h) = self.page_setup_handle(name) {
             ps.handle = h;
@@ -206,8 +224,12 @@ impl Scene {
         let handle = if let Some(ObjectType::Dictionary(d)) =
             self.document.objects.get_mut(&dict_handle)
         {
-            let h = d.entries.iter().find(|(k, _)| k == name).map(|(_, h)| *h);
-            d.entries.retain(|(k, _)| k != name);
+            let h = d
+                .entries
+                .iter()
+                .find(|(k, _)| k.eq_ignore_ascii_case(name))
+                .map(|(_, h)| *h);
+            d.entries.retain(|(k, _)| !k.eq_ignore_ascii_case(name));
             h
         } else {
             None
@@ -223,7 +245,8 @@ impl Scene {
         if old == new || new.trim().is_empty() {
             return;
         }
-        if self.page_setup_handle(new).is_some() {
+        // A different spelling of the same name is a rename, not a collision.
+        if !old.eq_ignore_ascii_case(new) && self.page_setup_handle(new).is_some() {
             return; // name collision
         }
         let Some(dict_handle) = self.plotsettings_dict_handle() else {
@@ -231,7 +254,7 @@ impl Scene {
         };
         let mut renamed = None;
         if let Some(ObjectType::Dictionary(d)) = self.document.objects.get_mut(&dict_handle) {
-            if let Some(e) = d.entries.iter_mut().find(|(k, _)| k == old) {
+            if let Some(e) = d.entries.iter_mut().find(|(k, _)| k.eq_ignore_ascii_case(old)) {
                 e.0 = new.to_string();
                 renamed = Some(e.1);
             }
diff --git a/src/scene/parametric_constraints.rs b/src/scene/parametric_constraints.rs
index 0dc086c20..0ab068550 100644
--- a/src/scene/parametric_constraints.rs
+++ b/src/scene/parametric_constraints.rs
@@ -244,6 +244,9 @@ pub(crate) fn set_polyline_vertex(
     x: f64,
     y: f64,
 ) -> bool {
+    let Some(index) = polyline_vertex_index(entity, index) else {
+        return false;
+    };
     match entity {
         acadrust::EntityType::LwPolyline(polyline) => polyline
             .vertices
@@ -800,9 +803,27 @@ pub(crate) fn resolve_point(entity: &acadrust::EntityType, marker: i32) -> Optio
     if marker < 0 {
         return None;
     }
-    super::dimension_assoc::source_points(entity)
-        .get(marker as usize)
-        .copied()
+    let points = super::dimension_assoc::source_points(entity);
+    // The closing segment of a closed polyline runs back to vertex 0, so its
+    // end marker (one past the last vertex) names that vertex — the same wrap
+    // the solver's `line_segment` applies.
+    let index = match polyline_vertex_index(entity, marker as usize) {
+        Some(index) => index,
+        None => marker as usize,
+    };
+    points.get(index).copied()
+}
+
+/// `marker` as a vertex index of a polyline, wrapping the closing segment's
+/// end (one past the last vertex) onto vertex 0 when the polyline is closed.
+/// `None` for anything that is not a 2D polyline.
+pub(crate) fn polyline_vertex_index(entity: &acadrust::EntityType, marker: usize) -> Option<usize> {
+    let (count, closed) = match entity {
+        acadrust::EntityType::LwPolyline(polyline) => (polyline.vertices.len(), polyline.is_closed),
+        acadrust::EntityType::Polyline2D(polyline) => (polyline.vertices.len(), polyline.is_closed()),
+        _ => return None,
+    };
+    Some(if closed && marker == count && count > 0 { 0 } else { marker })
 }
 
 /// Below this squared distance (1e-6 world units), two points count as
diff --git a/src/scene/parametric_solve.rs b/src/scene/parametric_solve.rs
index a0c7a1792..59a5d30ca 100644
--- a/src/scene/parametric_solve.rs
+++ b/src/scene/parametric_solve.rs
@@ -87,8 +87,16 @@ impl EntityGeom {
             (EntityGeom::Line(l), 0) => Some(l.p1),
             (EntityGeom::Line(l), 1) => Some(l.p2),
             (EntityGeom::Ray(l), 0) => Some(l.p1),
-            (EntityGeom::Polyline { points, .. }, marker) if marker >= 0 => {
-                points.get(marker as usize).copied()
+            (EntityGeom::Polyline { points, closed, .. }, marker) if marker >= 0 => {
+                // The closing segment's end marker (one past the last vertex)
+                // is vertex 0 on a closed polyline, as in `line_segment`.
+                let index = marker as usize;
+                let index = if *closed && index == points.len() && !points.is_empty() {
+                    0
+                } else {
+                    index
+                };
+                points.get(index).copied()
             }
             (EntityGeom::Circle(c), -3) => Some(c.center),
             (EntityGeom::Arc(a), 0) => Some(a.start),