diff --git a/geo/benches/prepared_geometry.rs b/geo/benches/prepared_geometry.rs
index e9d9b6b675..a9e0e83cc2 100644
--- a/geo/benches/prepared_geometry.rs
+++ b/geo/benches/prepared_geometry.rs
@@ -1,13 +1,48 @@
-use criterion::{criterion_group, criterion_main, Criterion};
+use criterion::{black_box, criterion_group, criterion_main, Criterion};
 use geo::algorithm::Relate;
 use geo::PreparedGeometry;
 use geo_types::MultiPolygon;
 
 fn criterion_benchmark(c: &mut Criterion) {
-    c.bench_function("relate prepared polygons", |bencher| {
-        let plot_polygons: MultiPolygon = geo_test_fixtures::nl_plots_wgs84();
-        let zone_polygons = geo_test_fixtures::nl_zones();
+    let plot_polygons: MultiPolygon = geo_test_fixtures::nl_plots_wgs84();
+    let zone_polygons = geo_test_fixtures::nl_zones();
+    c.bench_function("build prepared polygons", |bencher| {
+        bencher.iter(|| {
+            let plot_polygons = plot_polygons
+                .iter()
+                .map(PreparedGeometry::from)
+                .collect::<Vec<_>>();
+
+            let zone_polygons = zone_polygons
+                .iter()
+                .map(PreparedGeometry::from)
+                .collect::<Vec<_>>();
+
+            black_box((&plot_polygons, &zone_polygons));
+        });
+    });
+
+    c.bench_function("relate already prepared polygons", |bencher| {
+        let plot_polygons = plot_polygons
+            .iter()
+            .map(PreparedGeometry::from)
+            .collect::<Vec<_>>();
+
+        let zone_polygons = zone_polygons
+            .iter()
+            .map(PreparedGeometry::from)
+            .collect::<Vec<_>>();
+
+        bencher.iter(|| {
+            for a in &plot_polygons {
+                for b in &zone_polygons {
+                    black_box(a.relate(b).is_intersects());
+                }
+            }
+        });
+    });
 
+    c.bench_function("build and relate prepared polygons", |bencher| {
         bencher.iter(|| {
             let mut intersects = 0;
             let mut non_intersects = 0;
@@ -24,7 +59,7 @@ fn criterion_benchmark(c: &mut Criterion) {
 
             for a in &plot_polygons {
                 for b in &zone_polygons {
-                    if criterion::black_box(a.relate(b).is_intersects()) {
+                    if black_box(a.relate(b).is_intersects()) {
                         intersects += 1;
                     } else {
                         non_intersects += 1;
@@ -37,7 +72,9 @@ fn criterion_benchmark(c: &mut Criterion) {
         });
     });
 
-    c.bench_function("relate unprepared polygons", |bencher| {
+    let mut slow_group = c.benchmark_group("unprepared polygons");
+    slow_group.sample_size(10);
+    slow_group.bench_function("relate unprepared polygons", |bencher| {
         let plot_polygons: MultiPolygon = geo_test_fixtures::nl_plots_wgs84();
         let zone_polygons = geo_test_fixtures::nl_zones();
 
@@ -47,7 +84,7 @@ fn criterion_benchmark(c: &mut Criterion) {
 
             for a in &plot_polygons {
                 for b in &zone_polygons {
-                    if criterion::black_box(a.relate(b).is_intersects()) {
+                    if black_box(a.relate(b).is_intersects()) {
                         intersects += 1;
                     } else {
                         non_intersects += 1;
diff --git a/geo/src/algorithm/relate/geomgraph/index/prepared_geometry.rs b/geo/src/algorithm/relate/geomgraph/index/prepared_geometry.rs
index dfc01cf0e0..1663ac53bd 100644
--- a/geo/src/algorithm/relate/geomgraph/index/prepared_geometry.rs
+++ b/geo/src/algorithm/relate/geomgraph/index/prepared_geometry.rs
@@ -41,19 +41,8 @@ where
 {
     let mut geometry_graph = GeometryGraph::new(0, geometry.clone().into());
     let r_tree = geometry_graph.build_tree();
-    let envelope = r_tree.root().envelope();
-
-    // geo and rstar have different conventions for how to represet an empty bounding boxes
-    let bounding_rect: Option<Rect<F>> = if envelope == rstar::AABB::new_empty() {
-        None
-    } else {
-        Some(Rect::new(envelope.lower(), envelope.upper()))
-    };
-    // They should be equal - but we can save the computation in the `--release` case
-    // by using the bounding_rect from the RTree
-    debug_assert_eq!(bounding_rect, geometry_graph.geometry().bounding_rect());
-
     geometry_graph.set_tree(Rc::new(r_tree));
+    let bounding_rect = geometry_graph.geometry().bounding_rect();
 
     // TODO: don't pass in line intersector here - in theory we'll want pluggable line intersectors
     // and the type (Robust) shouldn't be hard coded here.
@@ -124,7 +113,7 @@ where
 mod tests {
     use super::*;
     use crate::algorithm::Relate;
-    use crate::polygon;
+    use crate::{polygon, wkt};
 
     #[test]
     fn relate() {
@@ -172,4 +161,44 @@ mod tests {
         assert_eq!(&poly, prepared_geom.geometry());
         assert_eq!(poly, prepared_geom.into_geometry());
     }
+
+    #[test]
+    fn zero_dimensional_point() {
+        let poly = polygon![(x: 0.0, y: 0.0), (x: 2.0, y: 0.0), (x: 1.0, y: 2.0)];
+        let prepared_poly = PreparedGeometry::from(&poly);
+        let point = crate::point!(x: 1.0, y: 1.0);
+        let prepared_point = PreparedGeometry::from(&point);
+
+        let im = poly.relate(&point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+
+        let im = prepared_poly.relate(&point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+
+        let im = poly.relate(&prepared_point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+
+        let im = prepared_poly.relate(&prepared_point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+    }
+
+    #[test]
+    fn zero_dimensional_multipoint() {
+        let poly = polygon![(x: 0.0, y: 0.0), (x: 2.0, y: 0.0), (x: 1.0, y: 2.0)];
+        let prepared_poly = PreparedGeometry::from(&poly);
+        let multi_point = wkt!(MULTIPOINT(1. 1.));
+        let prepared_multi_point = PreparedGeometry::from(&multi_point);
+
+        let im = poly.relate(&multi_point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+
+        let im = prepared_poly.relate(&multi_point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+
+        let im = poly.relate(&prepared_multi_point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+
+        let im = prepared_poly.relate(&prepared_multi_point);
+        assert!(im.matches("0F2FF1FF2").unwrap(), "got {im:?}");
+    }
 }