diff --git a/crates/fj-kernel/src/algorithms/approx/sketch.rs b/crates/fj-kernel/src/algorithms/approx/sketch.rs
index 873257a01..7748fb92a 100644
--- a/crates/fj-kernel/src/algorithms/approx/sketch.rs
+++ b/crates/fj-kernel/src/algorithms/approx/sketch.rs
@@ -12,9 +12,9 @@ impl Approx for &Sketch {
 
     fn approx_with_cache(
         self,
-        tolerance: impl Into<Tolerance>,
-        cache: &mut Self::Cache,
+        _tolerance: impl Into<Tolerance>,
+        _cache: &mut Self::Cache,
     ) -> Self::Approximation {
-        self.faces().approx_with_cache(tolerance, cache)
+        todo!()
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/sweep/sketch.rs b/crates/fj-kernel/src/algorithms/sweep/sketch.rs
index 4e8fb5789..c50b06777 100644
--- a/crates/fj-kernel/src/algorithms/sweep/sketch.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/sketch.rs
@@ -1,7 +1,7 @@
 use fj_math::Vector;
 
 use crate::{
-    objects::{Sketch, Solid},
+    objects::{Sketch, Solid, Surface},
     operations::Insert,
     services::Services,
     storage::Handle,
@@ -9,7 +9,7 @@ use crate::{
 
 use super::{Sweep, SweepCache};
 
-impl Sweep for Handle<Sketch> {
+impl Sweep for (Handle<Sketch>, Handle<Surface>) {
     type Swept = Handle<Solid>;
 
     fn sweep_with_cache(
@@ -21,7 +21,7 @@ impl Sweep for Handle<Sketch> {
         let path = path.into();
 
         let mut shells = Vec::new();
-        for face in self.faces().clone() {
+        for face in self.0.faces(self.1, services) {
             let shell = face.sweep_with_cache(path, cache, services);
             shells.push(shell);
         }
diff --git a/crates/fj-kernel/src/algorithms/transform/mod.rs b/crates/fj-kernel/src/algorithms/transform/mod.rs
index 2157917f4..da46c29ef 100644
--- a/crates/fj-kernel/src/algorithms/transform/mod.rs
+++ b/crates/fj-kernel/src/algorithms/transform/mod.rs
@@ -4,7 +4,6 @@ mod cycle;
 mod edge;
 mod face;
 mod shell;
-mod sketch;
 mod solid;
 mod surface;
 mod vertex;
diff --git a/crates/fj-kernel/src/algorithms/transform/sketch.rs b/crates/fj-kernel/src/algorithms/transform/sketch.rs
deleted file mode 100644
index 03b0e1387..000000000
--- a/crates/fj-kernel/src/algorithms/transform/sketch.rs
+++ /dev/null
@@ -1,21 +0,0 @@
-use fj_math::Transform;
-
-use crate::{objects::Sketch, services::Services};
-
-use super::{TransformCache, TransformObject};
-
-impl TransformObject for Sketch {
-    fn transform_with_cache(
-        self,
-        transform: &Transform,
-        services: &mut Services,
-        cache: &mut TransformCache,
-    ) -> Self {
-        let faces =
-            self.faces().into_iter().cloned().map(|face| {
-                face.transform_with_cache(transform, services, cache)
-            });
-
-        Self::new(faces)
-    }
-}
diff --git a/crates/fj-kernel/src/geometry/mod.rs b/crates/fj-kernel/src/geometry/mod.rs
index af0cf08f9..6d34554b1 100644
--- a/crates/fj-kernel/src/geometry/mod.rs
+++ b/crates/fj-kernel/src/geometry/mod.rs
@@ -1,4 +1,5 @@
 //! Types that are tied to objects, but aren't objects themselves
 
 pub mod curve;
+pub mod region;
 pub mod surface;
diff --git a/crates/fj-kernel/src/geometry/region.rs b/crates/fj-kernel/src/geometry/region.rs
new file mode 100644
index 000000000..7731a44c0
--- /dev/null
+++ b/crates/fj-kernel/src/geometry/region.rs
@@ -0,0 +1,77 @@
+//! A single, continues 2d region
+use fj_interop::mesh::Color;
+
+use crate::{
+    objects::{Cycle, Face, Surface},
+    operations::Insert,
+    services::Services,
+    storage::Handle,
+};
+
+/// A single, continuous 2d region, may contain holes. Once applied to a
+/// [`Surface`] becomes a [`Face`]
+///
+/// Interior cycles must have the opposite winding of the exterior cycle,
+/// meaning on the front side of the region, they must appear clockwise. This
+/// means that all [`HalfEdge`]s that bound a `Region` have the interior of the
+/// region on their left side (on the region's front side).
+///
+/// [`HalfEdge`]: crate::objects::HalfEdge
+#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
+pub struct Region {
+    exterior: Handle<Cycle>,
+    interiors: Vec<Handle<Cycle>>,
+    color: Option<Color>,
+}
+
+impl Region {
+    /// Construct an instance of `Region`
+    pub fn new(
+        exterior: Handle<Cycle>,
+        interiors: Vec<Handle<Cycle>>,
+        color: Option<Color>,
+    ) -> Self {
+        Self {
+            exterior,
+            interiors,
+            color,
+        }
+    }
+
+    /// Access the cycle that bounds the region on the outside
+    pub fn exterior(&self) -> &Handle<Cycle> {
+        &self.exterior
+    }
+
+    /// Access the cycles that bound the region on the inside
+    ///
+    /// Each of these cycles defines a hole in the region .
+    pub fn interiors(&self) -> impl Iterator<Item = &Handle<Cycle>> + '_ {
+        self.interiors.iter()
+    }
+
+    /// Access all cycles of the region (both exterior and interior)
+    pub fn all_cycles(&self) -> impl Iterator<Item = &Handle<Cycle>> + '_ {
+        [self.exterior()].into_iter().chain(self.interiors())
+    }
+
+    /// Access the color of the region
+    pub fn color(&self) -> Option<Color> {
+        self.color
+    }
+
+    /// Convert the 2D region to a 3D face, by applying it to a surface.
+    pub fn face(
+        &self,
+        surface: Handle<Surface>,
+        services: &mut Services,
+    ) -> Handle<Face> {
+        let face: Face = Face::new(
+            surface,
+            self.exterior().clone(),
+            self.interiors().cloned(),
+            self.color,
+        );
+        face.insert(services)
+    }
+}
diff --git a/crates/fj-kernel/src/objects/full/face.rs b/crates/fj-kernel/src/objects/full/face.rs
index 1b22a0962..2dd26e6da 100644
--- a/crates/fj-kernel/src/objects/full/face.rs
+++ b/crates/fj-kernel/src/objects/full/face.rs
@@ -4,6 +4,7 @@ use fj_interop::mesh::Color;
 use fj_math::Winding;
 
 use crate::{
+    geometry::region::Region,
     objects::{Cycle, Surface},
     storage::Handle,
 };
@@ -35,9 +36,7 @@ use crate::{
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Face {
     surface: Handle<Surface>,
-    exterior: Handle<Cycle>,
-    interiors: Vec<Handle<Cycle>>,
-    color: Option<Color>,
+    region: Region,
 }
 
 impl Face {
@@ -52,9 +51,7 @@ impl Face {
 
         Self {
             surface,
-            exterior,
-            interiors,
-            color,
+            region: Region::new(exterior, interiors, color),
         }
     }
 
@@ -65,24 +62,24 @@ impl Face {
 
     /// Access the cycle that bounds the face on the outside
     pub fn exterior(&self) -> &Handle<Cycle> {
-        &self.exterior
+        self.region.exterior()
     }
 
     /// Access the cycles that bound the face on the inside
     ///
     /// Each of these cycles defines a hole in the face.
     pub fn interiors(&self) -> impl Iterator<Item = &Handle<Cycle>> + '_ {
-        self.interiors.iter()
+        self.region.interiors()
     }
 
     /// Access all cycles of the face (both exterior and interior)
     pub fn all_cycles(&self) -> impl Iterator<Item = &Handle<Cycle>> + '_ {
-        [self.exterior()].into_iter().chain(self.interiors())
+        self.region.all_cycles()
     }
 
     /// Access the color of the face
     pub fn color(&self) -> Option<Color> {
-        self.color
+        self.region.color()
     }
 
     /// Determine handed-ness of the face's front-side coordinate system
diff --git a/crates/fj-kernel/src/objects/full/sketch.rs b/crates/fj-kernel/src/objects/full/sketch.rs
index 2f049a473..69003e279 100644
--- a/crates/fj-kernel/src/objects/full/sketch.rs
+++ b/crates/fj-kernel/src/objects/full/sketch.rs
@@ -1,5 +1,9 @@
+use std::collections::BTreeSet;
+
 use crate::{
-    objects::{Face, FaceSet},
+    geometry::region::Region,
+    objects::{FaceSet, Surface},
+    services::Services,
     storage::Handle,
 };
 
@@ -11,19 +15,26 @@ use crate::{
 /// currently validated.
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Sketch {
-    faces: FaceSet,
+    regions: BTreeSet<Region>,
 }
 
 impl Sketch {
     /// Construct an empty instance of `Sketch`
-    pub fn new(faces: impl IntoIterator<Item = Handle<Face>>) -> Self {
+    pub fn new(regions: impl IntoIterator<Item = Region>) -> Self {
         Self {
-            faces: faces.into_iter().collect(),
+            regions: regions.into_iter().collect(),
         }
     }
 
-    /// Access the faces of the sketch
-    pub fn faces(&self) -> &FaceSet {
-        &self.faces
+    /// Apply the regions of the sketch to some [`Surface`]
+    pub fn faces(
+        &self,
+        surface: Handle<Surface>,
+        services: &mut Services,
+    ) -> FaceSet {
+        self.regions
+            .iter()
+            .map(|r| r.face(surface.clone(), services))
+            .collect()
     }
 }