Are all polyhedrons are prisms and pyramids?

Answer 1

No, they are not There are many 3D shapes which are neither prisms nor pyramids.

A prism has flat, rectangular faces along its length and two ends, which can be triangular, square, hexagonal. An exception is the circular prism which is normally called a cylinder.

A pyramid may have any shape for its base, However if the base has 5 sides then the prism will be formed from 5 triangles rising from its base. A special case is the pyramid which has a circular base. We usually call it a cone.

Poly means many and hedron means sides, so a polyhedron is a 3D shape with many {usually flat) sides, which are more accurately called "faces" in mathematics. Hence an octahedron has eight faces. Imagine a pyramid (like the Egyption ones) with 4 triangular faces in the air and standing upon a fifth one (its base on the sand).

If you made two of such pyramids out of card and glued their square bases together, the remaining shape that we see is an octahedron. (Imagine that the glued bases are not there any more).