diff --git a/Cargo.lock b/Cargo.lock
index 75125075e..09dff2952 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -3513,6 +3513,13 @@ version = "0.9.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "49874b5167b65d7193b8aba1567f5c7d93d001cafc34600cee003eda787e483f"
 
+[[package]]
+name = "vertices-indices"
+version = "0.1.0"
+dependencies = [
+ "fj",
+]
+
 [[package]]
 name = "walkdir"
 version = "2.4.0"
diff --git a/Cargo.toml b/Cargo.toml
index cd3864d13..26b18ba89 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -15,6 +15,7 @@ members = [
     "models/spacer",
     "models/split",
     "models/star",
+    "models/vertices-indices",
 
     "tools/autolib",
     "tools/automator",
diff --git a/crates/fj-core/src/operations/build/shell.rs b/crates/fj-core/src/operations/build/shell.rs
index d77a4e435..0d4012c7e 100644
--- a/crates/fj-core/src/operations/build/shell.rs
+++ b/crates/fj-core/src/operations/build/shell.rs
@@ -1,13 +1,19 @@
+use std::collections::BTreeMap;
+
+use fj_interop::ext::ArrayExt;
 use fj_math::Point;
 
 use crate::{
-    objects::{Face, Shell},
+    geometry::CurveBoundary,
+    objects::{Curve, Face, HalfEdge, Shell, Surface, Vertex},
     operations::{
-        build::{BuildFace, Polygon},
+        build::{BuildFace, BuildHalfEdge, BuildSurface, Polygon},
         insert::{Insert, IsInserted, IsInsertedNo, IsInsertedYes},
         join::JoinCycle,
         reverse::ReverseCurveCoordinateSystems,
-        update::{UpdateCycle, UpdateFace, UpdateRegion},
+        update::{
+            UpdateCycle, UpdateFace, UpdateHalfEdge, UpdateRegion, UpdateShell,
+        },
     },
     services::Services,
 };
@@ -23,6 +29,96 @@ pub trait BuildShell {
         Shell::new([])
     }
 
+    /// Build a polyhedron by specifying its vertices and indices
+    fn from_vertices_and_indices(
+        vertices: impl IntoIterator<Item = impl Into<Point<3>>>,
+        indices: impl IntoIterator<Item = [usize; 3]>,
+        services: &mut Services,
+    ) -> Shell {
+        let vertices = vertices
+            .into_iter()
+            .enumerate()
+            .map(|(index, position)| {
+                let vertex = Vertex::new().insert(services);
+                let position = position.into();
+
+                (index, (vertex, position))
+            })
+            .collect::<BTreeMap<_, _>>();
+
+        let mut curves = BTreeMap::new();
+
+        let faces = indices
+            .into_iter()
+            .map(|indices| {
+                let [(a, a_pos), (b, b_pos), (c, c_pos)] = indices
+                    .map(|index| vertices.get(&index).expect("Invalid index"));
+
+                let (surface, _) = Surface::plane_from_points(
+                    [a_pos, b_pos, c_pos].map(Clone::clone),
+                );
+                let surface = surface.insert(services);
+
+                let curves_and_boundaries =
+                    [[a, b], [b, c], [c, a]].map(|vertices| {
+                        let vertices = vertices.map(Clone::clone);
+                        let vertices = CurveBoundary::<Vertex>::from(vertices);
+
+                        curves
+                            .get(&vertices.clone().reverse())
+                            .cloned()
+                            .unwrap_or_else(|| {
+                                let curve = Curve::new().insert(services);
+                                let boundary =
+                                    CurveBoundary::<Point<1>>::from([
+                                        [0.],
+                                        [1.],
+                                    ]);
+
+                                curves.insert(
+                                    vertices,
+                                    (curve.clone(), boundary),
+                                );
+
+                                (curve, boundary.reverse())
+                            })
+                    });
+
+                let half_edges = {
+                    let vertices = [a, b, c].map(Clone::clone);
+                    let [a, b, c] = [[0., 0.], [1., 0.], [0., 1.]];
+                    vertices
+                        .zip_ext([[a, b], [b, c], [c, a]])
+                        .zip_ext(curves_and_boundaries)
+                        .map(|((vertex, positions), (curve, boundary))| {
+                            HalfEdge::line_segment(
+                                positions,
+                                Some(boundary.reverse().inner),
+                                services,
+                            )
+                            .update_start_vertex(|_| vertex)
+                            .update_curve(|_| curve)
+                            .insert(services)
+                        })
+                };
+
+                Face::unbound(surface, services)
+                    .update_region(|region| {
+                        region
+                            .update_exterior(|cycle| {
+                                cycle
+                                    .add_half_edges(half_edges)
+                                    .insert(services)
+                            })
+                            .insert(services)
+                    })
+                    .insert(services)
+            })
+            .collect::<Vec<_>>();
+
+        Shell::empty().add_faces(faces)
+    }
+
     /// Build a tetrahedron from the provided points
     ///
     /// Accepts 4 points, naturally. For the purposes of the following
diff --git a/models/vertices-indices/Cargo.toml b/models/vertices-indices/Cargo.toml
new file mode 100644
index 000000000..33aff7f9a
--- /dev/null
+++ b/models/vertices-indices/Cargo.toml
@@ -0,0 +1,7 @@
+[package]
+name = "vertices-indices"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies.fj]
+path = "../../crates/fj"
diff --git a/models/vertices-indices/src/lib.rs b/models/vertices-indices/src/lib.rs
new file mode 100644
index 000000000..15050e57e
--- /dev/null
+++ b/models/vertices-indices/src/lib.rs
@@ -0,0 +1,21 @@
+use fj::core::{
+    objects::{Shell, Solid},
+    operations::{
+        build::{BuildShell, BuildSolid},
+        insert::Insert,
+        update::UpdateSolid,
+    },
+    services::Services,
+    storage::Handle,
+};
+
+pub fn model(services: &mut Services) -> Handle<Solid> {
+    Solid::empty()
+        .add_shells([Shell::from_vertices_and_indices(
+            [[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.]],
+            [[2, 1, 0], [0, 1, 3], [1, 2, 3], [2, 0, 3]],
+            services,
+        )
+        .insert(services)])
+        .insert(services)
+}
diff --git a/models/vertices-indices/src/main.rs b/models/vertices-indices/src/main.rs
new file mode 100644
index 000000000..2587df58c
--- /dev/null
+++ b/models/vertices-indices/src/main.rs
@@ -0,0 +1,8 @@
+use fj::{core::services::Services, handle_model};
+
+fn main() -> fj::Result {
+    let mut services = Services::new();
+    let model = vertices_indices::model(&mut services);
+    handle_model(model, services)?;
+    Ok(())
+}