Generalisation of the concept of angle

Question

The angle between two vectors is related to the scalar product as $\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \cos \gamma $, or the area of the triangle determined by the vectors as $\frac{1}{2}|\mathbf{a}| |\mathbf{b}| \sin \gamma$. I am wondering if there exists a generalisation of the angle concept to three vectors, perhaps using the triple product $(\mathbf{a} \times \mathbf{b})\cdot\mathbf{c}$?