4. There are the following four propositions:
(1) A pyramid with a base that is a regular polygon and all other faces being isosceles triangles is a regular pyramid.
(2) A triangular pyramid with a base that is an equilateral triangle and all dihedral angles between adjacent lateral faces being equal is a regular triangular pyramid.
(3) A hexahedron with two parallel faces and the other four faces being congruent isosceles trapezoids is a regular quadrilateral frustum.
(4) A polyhedron with two parallel faces and all other faces being parallelograms is a prism.
Among these, the number of correct propositions is ( ).
(A) 3
(B) 2
(C) 1
(D) 0
4. (D).

None of the four propositions are correct, and counterexamples are provided as follows:
(A) Counterexample: The base is an equilateral triangle with a side length of 3, the two side faces are isosceles triangles with side lengths of 3, 3, and 2, and one side face is an isosceles triangle with side lengths of 2, 2, and 3.
(B) Counterexample: Let $S^{\prime}-A B C$ be a regular tetrahedron, $\angle S A B>60^{\circ}$. Construct $B A^{\prime}=A B$, and connect $A^{\prime} C$. It can be proven that $\triangle A^{\prime} B C$ is an equilateral triangle. At this point, the tetrahedron $S^{\prime}-A^{\prime} B C$ satisfies the conditions but is not a regular tetrahedron.
(C) Counterexample: The figure obtained by translating one of the rectangles upwards.
(D) Counterexample: The concave decahedron as shown in the figure.