diff --git a/crates/ui-egui/src/dialogs/form.rs b/crates/ui-egui/src/dialogs/form.rs
index 40329c8c..fd14ff40 100644
--- a/crates/ui-egui/src/dialogs/form.rs
+++ b/crates/ui-egui/src/dialogs/form.rs
@@ -49,7 +49,7 @@ pub(super) fn length(ui: &mut egui::Ui, d: &mut Dialog, key: &str, unit: Unit, w
 fn lengths(kind: &str) -> &'static [&'static str] {
     match kind {
         "move" => &["dx", "dy"],
-        "rectangle" | "ellipse" | "rectangularGrid" | "artboardOptions" => &["width", "height"],
+        "rectangle" | "ellipse" | "rectangularGrid" | "polarGrid" | "artboardOptions" => &["width", "height"],
         "roundedRectangle" => &["width", "height", "radius"],
         "polygon" => &["radius"],
         "star" => &["radius1", "radius2"],
@@ -68,6 +68,7 @@ fn order(kind: &str) -> &'static [&'static str] {
         "offsetPath" => &["offset", "joins", "miterLimit"],
         "splitIntoGrid" => &["rows", "columns", "gutter"],
         "rectangularGrid" => &["width", "height", "rows", "columns"],
+        "polarGrid" => &["width", "height", "concentric", "radial"],
         "artboardOptions" => &["name", "width", "height"],
         _ => &[],
     }
@@ -182,6 +183,8 @@ pub(super) fn grid(ui: &mut egui::Ui, d: &mut Dialog, unit: Unit) {
                 let label = match (d.kind.as_str(), k.as_str()) {
                     ("rectangularGrid", "rows") => tl!("Horizontal Dividers:").into(),
                     ("rectangularGrid", "columns") => tl!("Vertical Dividers:").into(),
+                    ("polarGrid", "concentric") => tl!("Concentric Dividers:").into(),
+                    ("polarGrid", "radial") => tl!("Radial Dividers:").into(),
                     _ => humanized(&k),
                 };
                 field(ui, d, &k, &label);
diff --git a/crates/ui-egui/src/dialogs/mod.rs b/crates/ui-egui/src/dialogs/mod.rs
index 7ff56acb..85dff13b 100644
--- a/crates/ui-egui/src/dialogs/mod.rs
+++ b/crates/ui-egui/src/dialogs/mod.rs
@@ -209,7 +209,7 @@ macro_rules! registry {
 
 registry! {
     NewDocument: [new_document::KIND] => new_document::SPEC,
-    Shape: ["rectangle", "roundedRectangle", "ellipse", "polygon", "star", "lineSegment", "rectangularGrid"] => shapes::SPEC,
+    Shape: ["rectangle", "roundedRectangle", "ellipse", "polygon", "star", "lineSegment", "rectangularGrid", "polarGrid"] => shapes::SPEC,
     Transform: ["move", "rotate", "scale", "reflect", "shear"] => transform::SPEC,
     PathOp: ["average", "offsetPath", "simplify", "splitIntoGrid"] => path_ops::SPEC,
     DocumentSetup: ["documentSetup"] => document_setup::SPEC,
diff --git a/crates/ui-egui/src/dialogs/shapes.rs b/crates/ui-egui/src/dialogs/shapes.rs
index 56680c12..ac479732 100644
--- a/crates/ui-egui/src/dialogs/shapes.rs
+++ b/crates/ui-egui/src/dialogs/shapes.rs
@@ -17,6 +17,7 @@ fn title(kind: &str) -> &'static str {
         "polygon" => tl!("Polygon"),
         "star" => tl!("Star"),
         "rectangularGrid" => tl!("Rectangular Grid"),
+        "polarGrid" => tl!("Polar Grid"),
         _ => tl!("Line Segment Tool Options"),
     }
 }
@@ -35,6 +36,11 @@ fn confirm(app: &mut VectorcraftApp, d: &Dialog) -> Result<Value, String> {
             json!({"x": x, "y": y, "width": d.f64("width", 100.0), "height": d.f64("height", 100.0),
                 "rows": (d.f64("rows", 5.0) as u64).min(999), "columns": (d.f64("columns", 5.0) as u64).min(999)}),
         ),
+        "polarGrid" => (
+            "shape.polarGrid",
+            json!({"x": x, "y": y, "width": d.f64("width", 100.0), "height": d.f64("height", 100.0),
+                "concentric": (d.f64("concentric", 5.0) as u64).min(999), "radial": (d.f64("radial", 5.0) as u64).min(999)}),
+        ),
         "lineSegment" => {
             let (l, a) = (d.f64("length", 100.0), d.f64("angle", 0.0).to_radians());
             ("shape.line", json!({"x1": x, "y1": y, "x2": x + l * a.cos(), "y2": y - l * a.sin()}))
@@ -45,13 +51,13 @@ fn confirm(app: &mut VectorcraftApp, d: &Dialog) -> Result<Value, String> {
         ),
     };
     // On the active plane while the perspective grid shows, sized in plane units from the click.
-    let options = (d.kind == "rectangularGrid").then(|| json!({"rows": params["rows"], "columns": params["columns"]}));
+    let options = matches!(d.kind.as_str(), "rectangularGrid" | "polarGrid").then(|| params.clone());
     let result = match vectorcraft_engine::perspective_click(&app.session, id, &params, vectorcraft_geom::Point::new(x, y)) {
         Some((id, params)) => run_and_close(app, &id, params),
         None => run_and_close(app, id, params),
     }?;
     if let Some(options) = options {
-        app.run("tool.setOption", json!({"tool": "rectangularGrid", "values": options}))?;
+        app.run("tool.setOption", json!({"tool": d.kind, "values": options}))?;
     }
     Ok(result)
 }
diff --git a/crates/ui-egui/src/dialogs/tests.rs b/crates/ui-egui/src/dialogs/tests.rs
index 5095b7c0..cfba1dcb 100644
--- a/crates/ui-egui/src/dialogs/tests.rs
+++ b/crates/ui-egui/src/dialogs/tests.rs
@@ -41,6 +41,7 @@ fn kinds_map_to_their_dialogs() {
         ("roundedRectangle", DialogKind::Shape),
         ("lineSegment", DialogKind::Shape),
         ("rectangularGrid", DialogKind::Shape),
+        ("polarGrid", DialogKind::Shape),
         ("shear", DialogKind::Transform),
         ("splitIntoGrid", DialogKind::PathOp),
         ("artboardOptions", DialogKind::ArtboardOptions),
@@ -87,6 +88,7 @@ fn every_dialog_draws() {
         "star",
         "lineSegment",
         "rectangularGrid",
+        "polarGrid",
         "rotate",
         "reflect",
         "scale",
@@ -650,3 +652,72 @@ fn zig_zag_has_sliders_and_radio_buttons() {
     }
     assert!(!lines.contains(&"Ridges:"), "{lines:?}");
 }
+
+#[test]
+fn polar_grid_shared_canvas_click_defaults_units_counts_and_history() {
+    use vectorcraft_doc::NodeId;
+    use vectorcraft_tools::{PointerEvent, PointerKind};
+    let mut app = app();
+    app.select_tool("polarGrid");
+    app.run("tool.setOption", json!({"tool": "polarGrid", "values": {"concentric": 2, "radial": 3}})).unwrap();
+    let before = app.session.doc().unwrap().doc.clone();
+    let undo = app.session.doc().unwrap().history.undo.len();
+    for kind in [PointerKind::Down, PointerKind::Up] {
+        crate::canvas::dispatch(&mut app, &PointerEvent::new(kind, 30.0, 40.0), Default::default());
+    }
+    assert_eq!(DialogKind::of("polarGrid"), Some(DialogKind::Shape));
+    let d = app.ui.dialog.as_mut().expect("canvas click opens the shared shape form");
+    assert_eq!(d.fields["width"], json!("100 pt"));
+    assert_eq!(d.fields["height"], json!("100 pt"));
+    assert_eq!((d.fields["concentric"].clone(), d.fields["radial"].clone()), (json!(2), json!(3)));
+    d.fields.insert("width".into(), json!("25.4 mm"));
+    d.fields.insert("height".into(), json!("0.5 in"));
+    frame(&mut app, Default::default());
+    let result = confirm(&mut app).unwrap();
+    assert!(app.ui.dialog.is_none());
+    let s = app.session.doc().unwrap();
+    let group = s.doc.node(NodeId(result["id"].as_u64().unwrap())).unwrap();
+    let children = group.children().unwrap();
+    assert_eq!(children.len(), 6);
+    assert_eq!(children.iter().filter(|n| n.path_data().unwrap().is_closed()).count(), 3);
+    assert_eq!(s.history.undo.len(), undo + 1);
+    let made = s.doc.clone();
+    app.run("edit.undo", json!({})).unwrap();
+    assert_eq!(app.session.doc().unwrap().doc, before);
+    app.run("edit.redo", json!({})).unwrap();
+    assert_eq!(app.session.doc().unwrap().doc, made);
+}
+
+#[test]
+fn polar_grid_shared_cancel_reopen_zero_counts_and_failed_creation() {
+    let mut app = app();
+    app.run("tool.setOption", json!({"tool": "polarGrid", "values": {"concentric": 2, "radial": 3}})).unwrap();
+    let before = app.session.doc().unwrap().doc.clone();
+    open_tool_dialog(&mut app, "polarGrid", json!({"x": 10, "y": 20}));
+    let d = app.ui.dialog.as_mut().expect("shared Polar Grid form opens");
+    d.fields.insert("concentric".into(), json!(8));
+    cancel(&mut app);
+    assert_eq!(app.session.doc().unwrap().doc, before);
+    open_tool_dialog(&mut app, "polarGrid", json!({"x": 10, "y": 20}));
+    assert_eq!(app.ui.dialog.as_ref().unwrap().fields["concentric"], json!(2));
+    for key in ["concentric", "radial"] {
+        app.ui.dialog.as_mut().unwrap().fields.insert(key.into(), json!(0));
+    }
+    let result = confirm(&mut app).unwrap();
+    let group = app.session.doc().unwrap().doc.node(vectorcraft_doc::NodeId(result["id"].as_u64().unwrap())).unwrap();
+    assert_eq!(group.children().unwrap().len(), 1);
+    assert!(group.children().unwrap()[0].path_data().unwrap().is_closed());
+    open_tool_dialog(&mut app, "polarGrid", json!({"x": 10, "y": 20}));
+    assert_eq!(app.ui.dialog.as_ref().unwrap().fields["radial"], json!(0));
+    cancel(&mut app);
+    let layer = app.session.doc().unwrap().doc.layers[0].id;
+    app.run("layer.setProps", json!({"ids": [layer.0], "locked": true})).unwrap();
+    let options = app.session.tool_options_of("polarGrid");
+    let before = app.session.doc().unwrap().doc.clone();
+    open_tool_dialog(&mut app, "polarGrid", json!({"x": 10, "y": 20}));
+    app.ui.dialog.as_mut().unwrap().fields.insert("radial".into(), json!(9));
+    assert!(confirm(&mut app).is_err());
+    assert!(app.ui.dialog.is_none());
+    assert_eq!(app.session.tool_options_of("polarGrid"), options);
+    assert_eq!(app.session.doc().unwrap().doc, before);
+}
diff --git a/crates/ui-egui/src/dialogs/tools.rs b/crates/ui-egui/src/dialogs/tools.rs
index 88013a34..2697a48d 100644
--- a/crates/ui-egui/src/dialogs/tools.rs
+++ b/crates/ui-egui/src/dialogs/tools.rs
@@ -20,6 +20,13 @@ pub fn open_tool_dialog(app: &mut VectorcraftApp, kind: &str, p: Value) {
             let options = app.session.tool_options_of(kind);
             Dialog::new(kind, json!({"x": x, "y": y, "width": "100 pt", "height": "100 pt", "rows": options["rows"], "columns": options["columns"]}))
         }
+        "polarGrid" => {
+            let options = app.session.tool_options_of(kind);
+            Dialog::new(
+                kind,
+                json!({"x": x, "y": y, "width": "100 pt", "height": "100 pt", "concentric": options["concentric"], "radial": options["radial"]}),
+            )
+        }
         // Graph tool click: the graph's size.
         "graph" => Dialog::new(
             "command",
diff --git a/crates/ui-egui/src/i18n/cs.tsv b/crates/ui-egui/src/i18n/cs.tsv
index 440777bf..defd6191 100644
--- a/crates/ui-egui/src/i18n/cs.tsv
+++ b/crates/ui-egui/src/i18n/cs.tsv
@@ -4498,3 +4498,5 @@ mark-style	Japanese	Japonské
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	komprimovaný soubor se rozbalí na více, než VectorCraft přečte ({_1} MB dokumentu, {_2} MB na obrázek)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	dokument je příliš velký pro komprimované uložení ({0}): uložte ho s vypnutou volbou Použít kompresi
 @msg	the file stopped being read (please report this bug)	čtení souboru se přerušilo (nahlaste prosím tuto chybu)
+	Concentric Dividers:	Soustředné dělicí čáry:
+	Radial Dividers:	Radiální dělicí čáry:
diff --git a/crates/ui-egui/src/i18n/de.tsv b/crates/ui-egui/src/i18n/de.tsv
index e09d40f2..9f347288 100644
--- a/crates/ui-egui/src/i18n/de.tsv
+++ b/crates/ui-egui/src/i18n/de.tsv
@@ -4149,3 +4149,5 @@ theme	Appearance	Erscheinungsbild
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	die komprimierte Datei entpackt sich auf mehr, als VectorCraft liest ({_1} MB Dokument, {_2} MB pro Bild)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	das Dokument ist zu groß, um komprimiert gespeichert zu werden ({0}): speichern Sie es mit deaktivierter Option „Komprimierung verwenden“
 @msg	the file stopped being read (please report this bug)	das Lesen der Datei wurde abgebrochen (bitte melden Sie diesen Fehler)
+	Concentric Dividers:	Konzentrische Trennlinien:
+	Radial Dividers:	Radiale Trennlinien:
diff --git a/crates/ui-egui/src/i18n/es.tsv b/crates/ui-egui/src/i18n/es.tsv
index 833308da..4954d10a 100644
--- a/crates/ui-egui/src/i18n/es.tsv
+++ b/crates/ui-egui/src/i18n/es.tsv
@@ -4192,3 +4192,5 @@ lighting	Light	Luz
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	el archivo comprimido ocupa al descomprimirse más de lo que VectorCraft lee ({_1} MB de documento, {_2} MB por imagen)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	el documento es demasiado grande para guardarlo comprimido ({0}): guárdelo con Usar compresión desactivado
 @msg	the file stopped being read (please report this bug)	se dejó de leer el archivo (informe de este error)
+	Concentric Dividers:	Divisiones concéntricas:
+	Radial Dividers:	Divisiones radiales:
diff --git a/crates/ui-egui/src/i18n/fr.tsv b/crates/ui-egui/src/i18n/fr.tsv
index 5ad2bd5f..49139253 100644
--- a/crates/ui-egui/src/i18n/fr.tsv
+++ b/crates/ui-egui/src/i18n/fr.tsv
@@ -4202,3 +4202,5 @@ lighting	Light	Lumière
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	le fichier compressé dépasse une fois décompressé ce que VectorCraft lit ({_1} Mo de document, {_2} Mo par image)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	le document est trop volumineux pour être enregistré compressé ({0}) : enregistrez-le avec Utiliser la compression désactivé
 @msg	the file stopped being read (please report this bug)	la lecture du fichier s’est interrompue (veuillez signaler ce bogue)
+	Concentric Dividers:	Divisions concentriques :
+	Radial Dividers:	Divisions radiales :
diff --git a/crates/ui-egui/src/i18n/it.tsv b/crates/ui-egui/src/i18n/it.tsv
index 0cde4d46..2e924593 100644
--- a/crates/ui-egui/src/i18n/it.tsv
+++ b/crates/ui-egui/src/i18n/it.tsv
@@ -4194,3 +4194,5 @@ lighting	Light	Luce
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	il file compresso, una volta decompresso, supera ciò che VectorCraft legge ({_1} MB di documento, {_2} MB per immagine)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	il documento è troppo grande per essere salvato compresso ({0}): salvalo con Usa compressione disattivato
 @msg	the file stopped being read (please report this bug)	la lettura del file si è interrotta (segnala questo errore)
+	Concentric Dividers:	Divisori concentrici:
+	Radial Dividers:	Divisori radiali:
diff --git a/crates/ui-egui/src/i18n/ja.tsv b/crates/ui-egui/src/i18n/ja.tsv
index 6b05d121..4125621d 100644
--- a/crates/ui-egui/src/i18n/ja.tsv
+++ b/crates/ui-egui/src/i18n/ja.tsv
@@ -4188,3 +4188,5 @@ lighting	Light	ライト
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	圧縮ファイルを展開すると VectorCraft が読み込める量を超えます (ドキュメント {_1} MB、画像 1 枚あたり {_2} MB)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	ドキュメントが大きすぎて圧縮保存できません ({0}): 「圧縮を使用」をオフにして保存してください
 @msg	the file stopped being read (please report this bug)	ファイルの読み込みが中断されました (このバグを報告してください)
+	Concentric Dividers:	同心円の分割線:
+	Radial Dividers:	放射状の分割線:
diff --git a/crates/ui-egui/src/i18n/pt-br.tsv b/crates/ui-egui/src/i18n/pt-br.tsv
index c9d86310..04e66fd0 100644
--- a/crates/ui-egui/src/i18n/pt-br.tsv
+++ b/crates/ui-egui/src/i18n/pt-br.tsv
@@ -3677,3 +3677,5 @@ axis	Both	Ambos
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	o arquivo compactado se expande para mais do que o VectorCraft lê ({_1} MB de documento, {_2} MB por imagem)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	o documento é grande demais para ser salvo compactado ({0}): salve-o com Usar Compressão desativado
 @msg	the file stopped being read (please report this bug)	a leitura do arquivo foi interrompida (informe este erro)
+	Concentric Dividers:	Divisórias concêntricas:
+	Radial Dividers:	Divisórias radiais:
diff --git a/crates/ui-egui/src/i18n/ru.tsv b/crates/ui-egui/src/i18n/ru.tsv
index 4bab5e25..f95584f4 100644
--- a/crates/ui-egui/src/i18n/ru.tsv
+++ b/crates/ui-egui/src/i18n/ru.tsv
@@ -4190,3 +4190,5 @@ lighting	Light	Свет
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	сжатый файл распаковывается в объём больше, чем читает VectorCraft ({_1} МБ документа, {_2} МБ на изображение)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	документ слишком велик для сохранения со сжатием ({0}): сохраните его с выключенным параметром «Использовать сжатие»
 @msg	the file stopped being read (please report this bug)	чтение файла прервалось (пожалуйста, сообщите об этой ошибке)
+	Concentric Dividers:	Концентрические разделители:
+	Radial Dividers:	Радиальные разделители:
diff --git a/crates/ui-egui/src/i18n/uk.tsv b/crates/ui-egui/src/i18n/uk.tsv
index ea77f63b..489a369f 100644
--- a/crates/ui-egui/src/i18n/uk.tsv
+++ b/crates/ui-egui/src/i18n/uk.tsv
@@ -4174,3 +4174,5 @@ lighting	Light	Світло
 @msg	the compressed file unpacks to more than VectorCraft reads ({_1} MB of document, {_2} MB per image)	стислий файл розпаковується в обсяг більший, ніж читає VectorCraft ({_1} МБ документа, {_2} МБ на зображення)
 @msg	the document is too large to save compressed ({0}): save it with Use Compression off	документ завеликий для збереження зі стиском ({0}): збережіть його з вимкненим параметром «Використовувати стиск»
 @msg	the file stopped being read (please report this bug)	читання файлу перервалося (будь ласка, повідомте про цю помилку)
+	Concentric Dividers:	Концентричні розділювачі:
+	Radial Dividers:	Радіальні розділювачі:
diff --git a/crates/ui-egui/src/i18n/zh-hans.tsv b/crates/ui-egui/src/i18n/zh-hans.tsv
index 3a7a15b0..836b4259 100644
--- a/crates/ui-egui/src/i18n/zh-hans.tsv
+++ b/crates/ui-egui/src/i18n/zh-hans.tsv
@@ -3786,3 +3786,5 @@ lighting	Light	光源
 	Artistic	艺术效果
 	Film Grain…	胶片颗粒…
 	Highlight Area	高光区域
+	Concentric Dividers:	同心分隔线：
+	Radial Dividers:	径向分隔线：
diff --git a/crates/ui-egui/src/i18n/zh-hant.tsv b/crates/ui-egui/src/i18n/zh-hant.tsv
index 3bb7a640..2c962956 100644
--- a/crates/ui-egui/src/i18n/zh-hant.tsv
+++ b/crates/ui-egui/src/i18n/zh-hant.tsv
@@ -3567,3 +3567,5 @@ lighting	Light	光源
 	Artistic	藝術效果
 	Film Grain…	底片顆粒…
 	Highlight Area	亮部範圍
+	Concentric Dividers:	同心分隔線：
+	Radial Dividers:	徑向分隔線：