The state of matter you are referring to is solid. In solids, the particles are arranged closely together in a fixed and orderly pattern. This close arrangement allows them to touch each other, creating a strong intermolecular force that keeps them in place.
Particles in a solid vibrate around their fixed positions but do not move freely. This is why solids maintain a definite shape and volume. The vibrations are typically minimal compared to the movement of particles in liquids or gases, which means the overall structure of the solid remains stable.