diff --git a/fj/src/lib.rs b/fj/src/lib.rs
index 680d1926c..44f967bbc 100644
--- a/fj/src/lib.rs
+++ b/fj/src/lib.rs
@@ -16,7 +16,7 @@ mod syntax;
 
 pub mod prelude {
     pub use crate::syntax::{
-        Rotate as _, Sketch as _, Sweep as _, Translate as _, Union as _,
+        Group as _, Rotate as _, Sketch as _, Sweep as _, Translate as _,
     };
 }
 
diff --git a/fj/src/shape_3d.rs b/fj/src/shape_3d.rs
index 5c49d92e8..b9274089f 100644
--- a/fj/src/shape_3d.rs
+++ b/fj/src/shape_3d.rs
@@ -4,14 +4,14 @@ use crate::{Shape, Shape2d};
 #[derive(Clone, Debug)]
 #[repr(C)]
 pub enum Shape3d {
+    /// A group of two 3-dimensional shapes
+    Group(Box<Group>),
+
     /// A sweep of 2-dimensional shape along the z-axis
     Sweep(Sweep),
 
     /// A transformed 3-dimensional shape
     Transform(Box<Transform>),
-
-    /// The union of two 3-dimensional shapes
-    Union(Box<Union>),
 }
 
 impl From<Shape3d> for Shape {
@@ -20,6 +20,36 @@ impl From<Shape3d> for Shape {
     }
 }
 
+/// A group of two 3-dimensional shapes
+///
+/// A group is a collection of disjoint shapes. It is not a union, in that the
+/// shapes in the group are not allowed to touch or overlap.
+///
+/// # Limitations
+///
+/// Whether the shapes in the group touch or overlap is not currently checked.
+#[derive(Clone, Debug)]
+#[repr(C)]
+pub struct Group {
+    /// The first of the shapes
+    pub a: Shape3d,
+
+    /// The second of the shapes
+    pub b: Shape3d,
+}
+
+impl From<Group> for Shape {
+    fn from(shape: Group) -> Self {
+        Self::Shape3d(Shape3d::Group(Box::new(shape)))
+    }
+}
+
+impl From<Group> for Shape3d {
+    fn from(shape: Group) -> Self {
+        Self::Group(Box::new(shape))
+    }
+}
+
 /// A transformed 3-dimensional shape
 ///
 /// # Limitations
@@ -97,39 +127,3 @@ impl From<Sweep> for Shape3d {
         Self::Sweep(shape)
     }
 }
-
-/// The union of two 3-dimensional shapes
-///
-/// # Limitations
-///
-/// Support for unions is somewhat limited right now. A union of 2 distinct
-/// shapes doesn't really create a new shape, but just an aggregation of the
-/// two original shapes.
-///
-/// This means, for example, that generating the triangle mesh of the union does
-/// not result in a proper triangle mesh, but rather the two, possibly
-/// intersecting, triangle meshes of the original shapes.
-///
-/// See issue:
-/// <https://github.com/hannobraun/Fornjot/issues/42>
-#[derive(Clone, Debug)]
-#[repr(C)]
-pub struct Union {
-    /// The first of the shapes
-    pub a: Shape3d,
-
-    /// The second of the shapes
-    pub b: Shape3d,
-}
-
-impl From<Union> for Shape {
-    fn from(shape: Union) -> Self {
-        Self::Shape3d(Shape3d::Union(Box::new(shape)))
-    }
-}
-
-impl From<Union> for Shape3d {
-    fn from(shape: Union) -> Self {
-        Self::Union(Box::new(shape))
-    }
-}
diff --git a/fj/src/syntax.rs b/fj/src/syntax.rs
index b62a693cf..7c809c713 100644
--- a/fj/src/syntax.rs
+++ b/fj/src/syntax.rs
@@ -70,23 +70,23 @@ where
     }
 }
 
-pub trait Union {
-    fn union<Other>(&self, other: &Other) -> crate::Union
+pub trait Group {
+    fn group<Other>(&self, other: &Other) -> crate::Group
     where
         Other: Clone + Into<crate::Shape3d>;
 }
 
-impl<T> Union for T
+impl<T> Group for T
 where
     T: Clone + Into<crate::Shape3d>,
 {
-    fn union<Other>(&self, other: &Other) -> crate::Union
+    fn group<Other>(&self, other: &Other) -> crate::Group
     where
         Other: Clone + Into<crate::Shape3d>,
     {
         let a = self.clone().into();
         let b = other.clone().into();
 
-        crate::Union { a, b }
+        crate::Group { a, b }
     }
 }
diff --git a/models/csg-union-disjoint/README.md b/models/csg-union-disjoint/README.md
deleted file mode 100644
index 344c75907..000000000
--- a/models/csg-union-disjoint/README.md
+++ /dev/null
@@ -1,10 +0,0 @@
-# Fornjot - Disjoint Union
-
-A model that demonstrates [constructive solid geometry](https://en.wikipedia.org/wiki/Constructive_solid_geometry) (CSG) functionality, specifically the union of two disjoint bodies.
-
-To display this model, run the following from the repository root:
-``` sh
-cargo run -- --model csg-union-disjoint
-```
-
-![Screenshot of the disjoint union model](csg-union-disjoint.png)
diff --git a/models/csg-union-disjoint/Cargo.toml b/models/group/Cargo.toml
similarity index 78%
rename from models/csg-union-disjoint/Cargo.toml
rename to models/group/Cargo.toml
index 505071e7b..7910d2980 100644
--- a/models/csg-union-disjoint/Cargo.toml
+++ b/models/group/Cargo.toml
@@ -1,5 +1,5 @@
 [package]
-name    = "csg-union-disjoint"
+name    = "group"
 version = "0.1.0"
 edition = "2021"
 
diff --git a/models/group/README.md b/models/group/README.md
new file mode 100644
index 000000000..395f59b5f
--- /dev/null
+++ b/models/group/README.md
@@ -0,0 +1,10 @@
+# Fornjot - Group
+
+A model that demonstrates groups of two disjoint bodies.
+
+To display this model, run the following from the repository root:
+``` sh
+cargo run -- --model group
+```
+
+![Screenshot of the group model](group.png)
diff --git a/models/csg-union-disjoint/csg-union-disjoint.png b/models/group/group.png
similarity index 100%
rename from models/csg-union-disjoint/csg-union-disjoint.png
rename to models/group/group.png
diff --git a/models/csg-union-disjoint/src/lib.rs b/models/group/src/lib.rs
similarity index 84%
rename from models/csg-union-disjoint/src/lib.rs
rename to models/group/src/lib.rs
index bda316c43..1c16bccec 100644
--- a/models/csg-union-disjoint/src/lib.rs
+++ b/models/group/src/lib.rs
@@ -15,7 +15,7 @@ pub extern "C" fn model(_: &HashMap<String, String>) -> fj::Shape {
     let cube_a = fj::Sketch::from_points(vertices).sweep(1.0);
     let cube_b = cube_a.clone().translate([1.5, 0., 0.5]);
 
-    let disjoint_union = cube_a.union(&cube_b);
+    let group = cube_a.group(&cube_b);
 
-    disjoint_union.into()
+    group.into()
 }
diff --git a/src/kernel/shapes/union.rs b/src/kernel/shapes/group.rs
similarity index 93%
rename from src/kernel/shapes/union.rs
rename to src/kernel/shapes/group.rs
index 0bcdcb2b2..fe63c48ff 100644
--- a/src/kernel/shapes/union.rs
+++ b/src/kernel/shapes/group.rs
@@ -15,18 +15,13 @@ use crate::{
 
 use super::ToShape;
 
-impl ToShape for fj::Union {
+impl ToShape for fj::Group {
     fn to_shape(&self, tolerance: Scalar, debug_info: &mut DebugInfo) -> Shape {
         let mut shape = Shape::new();
 
         let a = self.a.to_shape(tolerance, debug_info);
         let b = self.b.to_shape(tolerance, debug_info);
 
-        // This doesn't create a true union, as it doesn't eliminate, merge, or
-        // split faces.
-        //
-        // See issue:
-        // https://github.com/hannobraun/Fornjot/issues/42
         copy_shape(a, &mut shape);
         copy_shape(b, &mut shape);
 
diff --git a/src/kernel/shapes/mod.rs b/src/kernel/shapes/mod.rs
index b3181a62d..700b07a0c 100644
--- a/src/kernel/shapes/mod.rs
+++ b/src/kernel/shapes/mod.rs
@@ -1,9 +1,9 @@
 pub mod circle;
 pub mod difference_2d;
+pub mod group;
 pub mod sketch;
 pub mod sweep;
 pub mod transform;
-pub mod union;
 
 use crate::{
     debug::DebugInfo,
@@ -53,9 +53,9 @@ macro_rules! dispatch {
             $(
                 fn $method(&self, $($arg_name: $arg_ty,)*) -> $ret {
                     match self {
+                        Self::Group(shape) => shape.$method($($arg_name,)*),
                         Self::Sweep(shape) => shape.$method($($arg_name,)*),
                         Self::Transform(shape) => shape.$method($($arg_name,)*),
-                        Self::Union(shape) => shape.$method($($arg_name,)*),
                     }
                 }
             )*