diff --git a/crates/xfdf/src/lib.rs b/crates/xfdf/src/lib.rs
index d839a052..f1ee4b15 100644
--- a/crates/xfdf/src/lib.rs
+++ b/crates/xfdf/src/lib.rs
@@ -264,6 +264,12 @@ fn xfdf_annots(doc: &Document, out: &mut String) {
                 }
                 out.push_str("</inklist>");
             }
+            // Polygon and polyline points (XFDF `<vertices>`: `x,y;x,y;…`).
+            let vertices = nums_of(doc, d.get(b"Vertices"));
+            let pts: Vec<String> = vertices.as_chunks::<2>().0.iter().map(|p| format!("{},{}", n(p[0]), n(p[1]))).collect();
+            if !pts.is_empty() {
+                let _ = write!(out, "<vertices>{}</vertices>", pts.join(";"));
+            }
             if let Some(pd) = d.get(b"Popup").map(|p| doc.resolve(p)).and_then(|p| p.as_dict().cloned()) {
                 let r = nums_of(doc, pd.get(b"Rect"));
                 if r.len() == 4 {
@@ -617,6 +623,14 @@ fn annot_from_xml(node: roxmltree::Node, subtype: &str, page_ref: ObjRef) -> Opt
                     .collect();
                 d.set(b"InkList".to_vec(), Object::Array(list));
             }
+            "vertices" => {
+                // Whole x,y pairs only; a stray trailing number is dropped.
+                let mut v = csv(child.text().unwrap_or(""));
+                v.truncate(v.len() - v.len() % 2);
+                if !v.is_empty() {
+                    d.set(b"Vertices".to_vec(), arr(&v));
+                }
+            }
             _ => {}
         }
     }
diff --git a/crates/xfdf/src/tests.rs b/crates/xfdf/src/tests.rs
index 371884de..022b36c6 100644
--- a/crates/xfdf/src/tests.rs
+++ b/crates/xfdf/src/tests.rs
@@ -352,3 +352,59 @@ fn reimporting_a_note_replaces_its_popup() {
     let parent = doc.get(popups[0]).as_dict().and_then(|d| d.reference(b"Parent")).unwrap();
     assert!(refs.contains(&parent), "the pop-up belongs to a note that is still on the page");
 }
+
+/// The `/Vertices` of every annotation on the document's pages, by subtype.
+fn vertices(doc: &Document) -> Vec<(String, Vec<f64>)> {
+    let mut out = Vec::new();
+    for p in pdfcraft_model::pages(doc) {
+        for a in p.dict.get(b"Annots").map(|a| doc.resolve(a)).and_then(|a| a.as_array().cloned()).unwrap_or_default() {
+            let Some(d) = doc.resolve(&a).as_dict().cloned() else { continue };
+            let sub = String::from_utf8_lossy(d.name(b"Subtype").unwrap_or_default()).into_owned();
+            let v = nums_of(doc, d.get(b"Vertices"));
+            if !v.is_empty() {
+                out.push((sub, v));
+            }
+        }
+    }
+    out
+}
+
+/// storytold/pdfcraft#809: XFDF exchange dropped polygon and polyline vertices, so the
+/// imported comments had no shape (and no appearance).
+#[test]
+fn xfdf_keeps_polygon_and_polyline_vertices() {
+    let mut src = blank();
+    let meta = |id: &str| Meta { date: Some("D:20261002120000Z".into()), id: id.into() };
+    let polygon = Shape::Polygon { vertices: vec![[100.0, 100.0], [200.0, 120.0], [150.0, 220.5]], cloud: false };
+    let polyline = Shape::PolyLine {
+        vertices: vec![[50.0, 300.0], [120.0, 380.0], [200.0, 310.0]],
+        start: pdfcraft_annot::LineEnding::None,
+        end: pdfcraft_annot::LineEnding::ClosedArrow,
+    };
+    for (page, shape, id) in [(0, polygon, "pg"), (1, polyline, "pl")] {
+        let new = NewAnnotation { page, style: Style::default_for(&shape), shape, contents: id.into(), author: "Ada".into() };
+        add_annotation(&mut src, &new, &meta(id)).unwrap();
+    }
+    let xfdf = export_xfdf(&src, true, false, "shapes.pdf");
+    assert!(xfdf.contains("<vertices>100,100;200,120;150,220.5</vertices>"), "{xfdf}");
+    assert!(xfdf.contains("<vertices>50,300;120,380;200,310</vertices>"), "{xfdf}");
+    let mut dst = blank();
+    let r = import(&mut dst, xfdf.as_bytes()).unwrap();
+    assert_eq!(r.comments, 2, "{r:?}");
+    assert_eq!(vertices(&dst), vertices(&src));
+    // The imported shapes are drawn again.
+    for p in pdfcraft_model::pages(&dst) {
+        for a in p.dict.get(b"Annots").map(|a| dst.resolve(a)).and_then(|a| a.as_array().cloned()).unwrap_or_default() {
+            let d = dst.resolve(&a).as_dict().cloned().unwrap();
+            assert!(d.get(b"AP").is_some(), "{d:?}");
+        }
+    }
+    // Acrobat-style input: a stray trailing number is dropped and only whole points are kept.
+    let odd = r#"<?xml version="1.0"?><xfdf xmlns="http://ns.adobe.com/xfdf/"><annots>
+        <polygon page="0" rect="0,0,50,50" name="odd"><vertices>1,2;3,4;5,6;7</vertices></polygon>
+        <polygon page="0" rect="0,0,50,50" name="none"><vertices>junk</vertices></polygon>
+        </annots></xfdf>"#;
+    let mut dst = blank();
+    import(&mut dst, odd.as_bytes()).unwrap();
+    assert_eq!(vertices(&dst), vec![("Polygon".to_string(), vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0])]);
+}