diff --git a/src/kernel/geometry/curves/circle.rs b/src/kernel/geometry/curves/circle.rs
index 966e7896a..f9c292576 100644
--- a/src/kernel/geometry/curves/circle.rs
+++ b/src/kernel/geometry/curves/circle.rs
@@ -3,7 +3,7 @@ use std::f64::consts::PI;
 use crate::math::{Point, Scalar, Transform, Vector};
 
 /// A circle
-#[derive(Clone, Copy, Debug, PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Circle {
     /// The center point of the circle
     pub center: Point<3>,
diff --git a/src/kernel/geometry/curves/line.rs b/src/kernel/geometry/curves/line.rs
index ec85f9d8c..1e1795ff3 100644
--- a/src/kernel/geometry/curves/line.rs
+++ b/src/kernel/geometry/curves/line.rs
@@ -1,7 +1,7 @@
 use crate::math::{Point, Transform, Vector};
 
 /// A line, defined by a point and a vector
-#[derive(Clone, Copy, Debug, PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Line {
     /// The origin of the line's coordinate system
     pub origin: Point<3>,
diff --git a/src/kernel/geometry/curves/mod.rs b/src/kernel/geometry/curves/mod.rs
index 6c2b3c286..513d4a3c7 100644
--- a/src/kernel/geometry/curves/mod.rs
+++ b/src/kernel/geometry/curves/mod.rs
@@ -14,7 +14,7 @@ pub use self::{circle::Circle, line::Line};
 /// The nomenclature is inspired by Boundary Representation Modelling Techniques
 /// by Ian Stroud. "Curve" refers to unbounded one-dimensional geometry, while
 /// while edges are bounded portions of curves.
-#[derive(Clone, Debug, PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub enum Curve {
     /// A circle
     Circle(Circle),
diff --git a/src/kernel/geometry/surfaces/mod.rs b/src/kernel/geometry/surfaces/mod.rs
index c12222b74..d1f3d360c 100644
--- a/src/kernel/geometry/surfaces/mod.rs
+++ b/src/kernel/geometry/surfaces/mod.rs
@@ -12,7 +12,7 @@ use crate::{
 use super::{Curve, Line};
 
 /// A two-dimensional shape
-#[derive(Clone, Debug, PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub enum Surface {
     /// A swept curve
     Swept(Swept),
diff --git a/src/kernel/geometry/surfaces/swept.rs b/src/kernel/geometry/surfaces/swept.rs
index ecf5c2bb5..447f5c6db 100644
--- a/src/kernel/geometry/surfaces/swept.rs
+++ b/src/kernel/geometry/surfaces/swept.rs
@@ -4,7 +4,7 @@ use crate::{
 };
 
 /// A surface that was swept from a curve
-#[derive(Clone, Debug, PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Swept {
     /// The curve that this surface was swept from
     pub curve: Curve,
diff --git a/src/kernel/topology/edges.rs b/src/kernel/topology/edges.rs
index 99591ed8b..d7b5b6a3c 100644
--- a/src/kernel/topology/edges.rs
+++ b/src/kernel/topology/edges.rs
@@ -6,7 +6,7 @@ use crate::{
 use super::vertices::Vertex;
 
 /// The edges of a shape
-#[derive(Clone)]
+#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Edges {
     /// The cycles that the edges of the shape form
     ///
@@ -34,13 +34,13 @@ impl Edges {
 /// The end of each edge in the cycle must connect to the beginning of the next
 /// edge. The end of the last edge must connect to the beginning of the first
 /// one.
-#[derive(Clone)]
+#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Cycle {
     pub edges: Vec<Edge>,
 }
 
 /// An edge of a shape
-#[derive(Clone, Debug)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Edge {
     /// The curve that defines the edge's geometry
     ///
diff --git a/src/kernel/topology/faces.rs b/src/kernel/topology/faces.rs
index 2063faf8b..ebe9a0dea 100644
--- a/src/kernel/topology/faces.rs
+++ b/src/kernel/topology/faces.rs
@@ -17,7 +17,7 @@ use crate::{
 use super::edges::Edges;
 
 /// The faces of a shape
-#[derive(Clone)]
+#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Faces(pub Vec<Face>);
 
 impl Faces {
@@ -34,7 +34,7 @@ impl Faces {
 }
 
 /// A face of a shape
-#[derive(Clone)]
+#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub enum Face {
     /// A face of a shape
     ///