diff --git a/data-model.d.ts b/data-model.d.ts
index 6fff406..c2ac4a3 100644
--- a/data-model.d.ts
+++ b/data-model.d.ts
@@ -10,7 +10,7 @@
  * @see DefaultGraph
  * @see BaseQuad
  */
-export type Term = NamedNode | BlankNode | Literal | Variable | DefaultGraph | BaseQuad;
+export type Term = NamedNode | BlankNode | Literal | Variable | DefaultGraph | BaseQuad | BaseTriple;
 
 /**
  * Contains an IRI.
@@ -128,12 +128,12 @@ export interface DefaultGraph {
 }
 
 /**
- * The subject, which is a NamedNode, BlankNode or Variable.
+ * The subject, which is a NamedNode, BlankNode, Variable, or a quoted triple.
  * @see NamedNode
  * @see BlankNode
  * @see Variable
  */
-export type Quad_Subject = NamedNode | BlankNode | Quad | Variable;
+export type Quad_Subject = NamedNode | BlankNode | Triple | Variable;
 
 /**
  * The predicate, which is a NamedNode or Variable.
@@ -143,13 +143,13 @@ export type Quad_Subject = NamedNode | BlankNode | Quad | Variable;
 export type Quad_Predicate = NamedNode | Variable;
 
 /**
- * The object, which is a NamedNode, Literal, BlankNode or Variable.
+ * The object, which is a NamedNode, Literal, BlankNode, Variable, or a quoted triple.
  * @see NamedNode
  * @see Literal
  * @see BlankNode
  * @see Variable
  */
-export type Quad_Object = NamedNode | Literal | BlankNode | Quad | Variable;
+export type Quad_Object = NamedNode | Literal | BlankNode | Triple | Variable;
 
 /**
  * The named graph, which is a DefaultGraph, NamedNode, BlankNode or Variable.
@@ -233,6 +233,13 @@ export interface Quad extends BaseQuad {
     equals(other: Term | null | undefined): boolean;
 }
 
+export interface BaseTriple extends Omit<BaseQuad, 'graph' | 'termType'> {
+    termType: 'QuotedTriple';
+}
+export interface Triple extends Omit<Quad, 'graph' | 'termType'> {
+    termType: 'QuotedTriple';
+}
+
 /**
  * A factory for instantiating RDF terms and quads.
  */
@@ -286,5 +293,5 @@ export interface DataFactory<OutQuad extends BaseQuad = Quad, InQuad extends Bas
      * @return A new instance of Quad.
      * @see Quad
      */
-    quad(subject: InQuad['subject'], predicate: InQuad['predicate'], object: InQuad['object'], graph?: InQuad['graph']): OutQuad;
+    quad(subject: InQuad['subject'] | InQuad, predicate: InQuad['predicate'], object: InQuad['object'] | InQuad, graph?: InQuad['graph']): OutQuad;
 }
diff --git a/rdf-js-tests.ts b/rdf-js-tests.ts
index af12b23..6a5c0e0 100644
--- a/rdf-js-tests.ts
+++ b/rdf-js-tests.ts
@@ -1,5 +1,5 @@
 import { BlankNode, DataFactory, Dataset, DatasetCore, DatasetCoreFactory, DatasetFactory, DefaultGraph, Literal,
-  NamedNode, Quad, BaseQuad, Sink, Source, Store, Stream, Term, Variable, Quad_Graph } from ".";
+  NamedNode, Quad, BaseQuad, Sink, Source, Store, Stream, Term, Variable, Quad_Graph, Triple, BaseTriple } from ".";
 import { EventEmitter } from "events";
 
 function test_terms() {
@@ -54,6 +54,32 @@ function test_terms() {
     let defaultGraphEqual: boolean = defaultGraph.equals(someTerm);
     defaultGraphEqual = defaultGraph.equals(null);
     defaultGraphEqual = defaultGraph.equals(undefined);
+
+    const term: Term = <any> {};
+    let term2: Term | undefined
+    switch (term.termType) {
+        case 'Quad':
+            term2 = <BaseQuad>term;
+            break;
+        case 'QuotedTriple':
+            term2 = <BaseTriple>term;
+            break;
+        case 'NamedNode':
+            term2 = <NamedNode>term;
+            break;
+        case 'Literal':
+            term2 = <Literal>term;
+            break;
+        case 'BlankNode':
+            term2 = <BlankNode>term;
+            break;
+        case 'Variable':
+            term2 = <Variable>term;
+            break;
+        case 'DefaultGraph':
+            term2 = <DefaultGraph>term;
+            break;
+    }
 }
 
 function test_quads() {
@@ -113,11 +139,15 @@ function test_datafactory_star() {
     );
 
     // Decompose the triple
-    if (quadBobAgeCertainty.subject.termType === 'Quad') {
-        const quadBobAge2: Quad = quadBobAgeCertainty.subject;
+    if (quadBobAgeCertainty.subject.termType === 'QuotedTriple') {
+        const quadBobAge2: Triple = quadBobAgeCertainty.subject;
 
         const equalToSelf: boolean = quadBobAge2.equals(quadBobAge);
         const notEqualToOtherType: boolean = quadBobAge2.equals(dataFactory.namedNode('ex:something:else'));
+
+        const dataset: DatasetCore = <any> {};
+        // @ts-expect-error: triple is not assignable to quad. It has no graph property
+        dataset.add(quadBobAge2);
     }
 }
 
@@ -137,11 +167,15 @@ function test_datafactory_star_basequad() {
     );
 
     // Decompose the triple
-    if (quadBobAgeCertainty.subject.termType === 'Quad') {
-        const quadBobAge2: BaseQuad = quadBobAgeCertainty.subject;
+    if (quadBobAgeCertainty.subject.termType === 'QuotedTriple') {
+        const quadBobAge2: BaseTriple = quadBobAgeCertainty.subject;
 
         const equalToSelf: boolean = quadBobAge2.equals(quadBobAge);
         const notEqualToOtherType: boolean = quadBobAge2.equals(dataFactory.namedNode('ex:something:else'));
+
+        const dataset: DatasetCore<BaseQuad> = <any> {};
+        // @ts-expect-error: triple is not assignable to quad. It has no graph property
+        dataset.add(quadBobAge2);
     }
 }