diff --git a/code/AssetLib/glTF2/glTF2Importer.cpp b/code/AssetLib/glTF2/glTF2Importer.cpp
index 9ce488cbd..0b784e0d4 100644
--- a/code/AssetLib/glTF2/glTF2Importer.cpp
+++ b/code/AssetLib/glTF2/glTF2Importer.cpp
@@ -574,7 +574,7 @@ void glTF2Importer::ImportMeshes(glTF2::Asset &r) {
 					case PrimitiveMode_TRIANGLE_FAN:
 						nFaces = count - 2;
 						facePtr = faces = new aiFace[nFaces];
-						SetFaceAndAdvance(facePtr, data.GetUInt(0), data.GetUInt(1), data.GetUInt(2));
+						SetFaceAndAdvance(facePtr, aim->mNumVertices, data.GetUInt(0), data.GetUInt(1), data.GetUInt(2));
 						for (unsigned int i = 1; i < nFaces; ++i) {
 							SetFaceAndAdvance(facePtr, aim->mNumVertices, faces[0].mIndices[0], faces[i - 1].mIndices[2], data.GetUInt(i + 2));
 						}
@@ -664,7 +664,11 @@ void glTF2Importer::ImportMeshes(glTF2::Asset &r) {
 				aim->mFaces = faces;
                 const unsigned int actualNumFaces = static_cast<unsigned int>(facePtr - faces);
 				if (actualNumFaces < nFaces) {
-					ASSIMP_LOG_WARN("Some faces had out-of-range indices. Those faces were dropped.");
+					ASSIMP_LOG_WARN("Some faces in mesh had out-of-range indices. Those faces were dropped.");
+				}
+				if (actualNumFaces == 0)
+				{
+					throw DeadlyImportError(std::string("Mesh \"") + aim->mName.C_Str() + "\" has no faces");
 				}
 				aim->mNumFaces = actualNumFaces;
 				ai_assert(CheckValidFacesIndices(faces, actualNumFaces, aim->mNumVertices));
diff --git a/test/unit/utglTF2ImportExport.cpp b/test/unit/utglTF2ImportExport.cpp
index 8bc20e950..c3ad2d994 100644
--- a/test/unit/utglTF2ImportExport.cpp
+++ b/test/unit/utglTF2ImportExport.cpp
@@ -46,11 +46,13 @@ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 #include <assimp/scene.h>
 #include <assimp/Exporter.hpp>
 #include <assimp/Importer.hpp>
+#include <assimp/LogStream.hpp>
+#include <assimp/DefaultLogger.hpp>
+
 
 #include <array>
 
 #include <assimp/pbrmaterial.h>
-
 using namespace Assimp;
 
 class utglTF2ImportExport : public AbstractImportExportBase {
@@ -542,14 +544,11 @@ TEST_F(utglTF2ImportExport, norootnode_issue_3269) {
     ASSERT_EQ(scene, nullptr);
 }
 
-#include <assimp/LogStream.hpp>
-#include <assimp/DefaultLogger.hpp>
-
 TEST_F(utglTF2ImportExport, indexOutOfRange) {
     // The contents of an asset should not lead to an assert.
     Assimp::Importer importer;
 
-    struct WarningObserver : Assimp::LogStream
+    struct LogObserver : Assimp::LogStream
     {
         bool m_observedWarning = false;
         void write(const char *message) override
@@ -557,15 +556,23 @@ TEST_F(utglTF2ImportExport, indexOutOfRange) {
             m_observedWarning = m_observedWarning || std::strstr(message, "faces were dropped");
         }
     };
-    WarningObserver warningObserver;
+    LogObserver logObserver;
     
-    DefaultLogger::get()->attachStream(&warningObserver);
+    DefaultLogger::get()->attachStream(&logObserver);
     const aiScene *scene = importer.ReadFile(ASSIMP_TEST_MODELS_DIR "/glTF2/IndexOutOfRange/IndexOutOfRange.gltf", aiProcess_ValidateDataStructure);
     ASSERT_NE(scene, nullptr);
     ASSERT_NE(scene->mRootNode, nullptr);
     ASSERT_EQ(scene->mNumMeshes, 1);
     EXPECT_EQ(scene->mMeshes[0]->mNumFaces, 11);
-    DefaultLogger::get()->detachStream(&warningObserver);
-    EXPECT_TRUE(warningObserver.m_observedWarning);
+    DefaultLogger::get()->detachStream(&logObserver);
+    EXPECT_TRUE(logObserver.m_observedWarning);
 }
 
+TEST_F(utglTF2ImportExport, allIndicesOutOfRange) {
+    // The contents of an asset should not lead to an assert.
+    Assimp::Importer importer;
+    const aiScene *scene = importer.ReadFile(ASSIMP_TEST_MODELS_DIR "/glTF2/IndexOutOfRange/AllIndicesOutOfRange.gltf", aiProcess_ValidateDataStructure);
+    ASSERT_EQ(scene, nullptr);
+    std::string error = importer.GetErrorString();
+    ASSERT_NE(error.find("Mesh \"Mesh\" has no faces"), std::string::npos);
+}