There are a few families of polyhedra with identical faces.
There are none whose faces have 6 or more sides.
There is no special name for polyhedra whose faces are pentagons or pentagrams. A dodecahedron is an example.
If coplanar faces are disallowed, the only polyhedron with quadrilateral faces are the cube and rhombohedron.
There are infinitely many polyhedra with equilateral triangular faces: the tetrahedron, octahedron and icosahedron are examples.
Prisms are three dimensional figures that always have two congruent faces. The congruent faces are also parallel to one another.
It is a cube
cuboid
A cuboid.
A cuboid.
A cube
A cube would fit the given description
A square is not a solid figure at all. It's a flat figure, with four congruent faces and four congruent angles.
A triangular prism would fit the given description
All three dimensional figures have more faces than a one dimensional figure. There are an infinite number of one dimensional points on a three dimensional figure
Pyramid
cube