diff --git a/CHANGELOG.md b/CHANGELOG.md
index 13971714..cb034e03 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+### Added
+
+- Add official support for Frustum, Pyramid, and Wedge geometries.
+
 ### Changed
 
 - Improved unit tests for `Meshes.Cylinder` and `Meshes.CylinderSurface` ([GitHub Issue #67](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/67)).
diff --git a/docs/src/support.md b/docs/src/support.md
index be77983c..0626a5fc 100644
--- a/docs/src/support.md
+++ b/docs/src/support.md
@@ -41,7 +41,7 @@ designed to check for accuracy.
 | `CylinderSurface` | ⚠️ | ✅ | ✅ |
 | `Disk` | ⚠️ | ✅ | ✅ |
 | `Ellipsoid` | ✅ | ✅ | ✅ |
-| `Frustum` | 🛑 | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) |
+| `Frustum` | ⚠️ | ✅ | ✅ |
 | `FrustumSurface` | ⚠️ | ✅ | ✅ |
 | `Hexahedron` | ✅ | ✅ | ✅ |
 | `Line` | ✅ | ✅ | ✅ |
@@ -49,7 +49,7 @@ designed to check for accuracy.
 | `ParametrizedCurve` | ✅ | ✅ | ✅ |
 | `Plane` | ✅ | ✅ | ✅ |
 | `Polyarea` | 🛑 | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) |
-| `Pyramid` | 🛑 | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) |
+| `Pyramid` | ⚠️ | ✅ | ✅ |
 | `Quadrangle` | ⚠️ | ✅ | ✅ |
 | `Ray` | ✅ | ✅ | ✅ |
 | `Ring` | ✅ | ✅ | ✅ |
@@ -61,7 +61,7 @@ designed to check for accuracy.
 | `Tetrahedron` | ⚠️ | ✅ | ✅ |
 | `Triangle` | ✅ | ✅ | ✅ |
 | `Torus` | ⚠️ | ✅ | ✅ |
-| `Wedge` | 🛑 | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) | [🎗️](https://github.com/JuliaGeometry/MeshIntegrals.jl/issues/28) |
+| `Wedge` | ⚠️ | ✅ | ✅ |
 
 | Symbol | Support Level |
 |--------|---------|
diff --git a/test/combinations.jl b/test/combinations.jl
index 4a57bbb3..d22a77e8 100644
--- a/test/combinations.jl
+++ b/test/combinations.jl
@@ -422,6 +422,31 @@ end
     runtests(testable; rtol = 1e-2)
 end
 
+@testitem "Meshes.Frustum" setup=[Combinations] begin
+    if pkgversion(Meshes) >= v"0.52.12"
+        # Geometry
+        r = 2.5u"m"
+        h = 3.5u"m"
+        origin = Point(0, 0, 0)
+        midpoint = Point(0.0u"m", 0.0u"m", 0.5 * h)
+        apex = Point(0.0u"m", 0.0u"m", h)
+        ẑ = Vec(0, 0, 1)
+        xy_plane = Plane(origin, ẑ)
+        base = Disk(xy_plane, r)
+        mid_plane = Plane(midpoint, ẑ)
+        mid_disk = Disk(mid_plane, 0.5 * r)
+        frustum = Frustum(base, mid_disk)
+
+        # Integrand & Solution
+        integrand(p) = 1.0u"A"
+        solution = (7 // 8) * (π * r^2 * h / 3) * u"A"
+
+        # Package and run tests
+        testable = TestableGeometry(integrand, frustum, solution)
+        runtests(testable)
+    end
+end
+
 @testitem "Meshes.FrustumSurface" setup=[Combinations] begin
     # Geometry
     # Create a frustum whose radius halves at the top, i.e. the bottom half of a cone
@@ -491,6 +516,7 @@ end
 end
 
 @testitem "Meshes.ParaboloidSurface" setup=[Combinations] begin
+    # Geometry
     origin = Point(0, 0, 0)
     parab = ParaboloidSurface(origin, 2.5, 4.15)
 
@@ -546,6 +572,26 @@ end
     runtests(testable)
 end
 
+@testitem "Meshes.Pyramid" setup=[Combinations] begin
+    if pkgversion(Meshes) >= v"0.52.12"
+        # Geometry
+        a = Point(-1, -1, 0)
+        b = Point(1, -1, 0)
+        c = Point(1, 1, 0)
+        d = Point(-1, 1, 0)
+        apex = Point(0, 0, 1)
+        pyramid = Pyramid(a, b, c, d, apex)
+        # Integrand & Solution
+        integrand(p) = 1.0u"A"
+        w = norm(b - a)
+        h = norm(d - a)
+        solution = (1 // 3) * w * h * u"A*m"
+        # Package and run tests
+        testable = TestableGeometry(integrand, pyramid, solution)
+        runtests(testable)
+    end
+end
+
 @testitem "Meshes.Quadrangle" setup=[Combinations] begin
     using SpecialFunctions: erf
 
@@ -739,3 +785,27 @@ end
     testable = TestableGeometry(integrand, triangle, solution)
     runtests(testable)
 end
+
+@testitem "Meshes.Wedge" setup=[Combinations] begin
+    if pkgversion(Meshes) >= v"0.52.12"
+        # Geometry
+        a₀ = Point(0, 0, 0)
+        b₀ = Point(1, 0, 0)
+        c₀ = Point(0, 1, 0)
+        a₁ = Point(0, 0, 1)
+        b₁ = Point(1, 0, 1)
+        c₁ = Point(0, 1, 1)
+        wedge = Wedge(a₀, b₀, c₀, a₁, b₁, c₁)
+
+        # Integrand & Solution
+        function integrand(p::Meshes.Point)
+            x, y, z = ustrip.(u"m", to(p))
+            (x + 2y + 3z) * u"A"
+        end
+        solution = (5 // 4) * u"A*m^3"
+
+        # Package and run tests
+        testable = TestableGeometry(integrand, wedge, solution)
+        runtests(testable)
+    end
+end