4. In a triangular pyramid, two of the three faces are isosceles right triangles, and the other is an equilateral triangle with a side length of 1. Then, the number of such triangular pyramids is $\qquad$.
4. 3 cases concerning the tetrahedron $ABCD$ are as follows:
(1) $AB=AC=BC=AD=1, CD=BD=\sqrt{2}$;
(2) $BC=BD=CD=1, AB=AC=AD=\frac{\sqrt{2}}{2}$;
(3) $AB=BC=AC=AD=BD=1, CD=\sqrt{2}$.