Allotropes are different forms of the same element that exist in the same physical state but have distinct structures and properties. For example, carbon can exist as diamond, which is hard and transparent, or as graphite, which is soft and opaque. These variations arise from the way atoms are arranged and bonded together. The concept of allotropes is important in chemistry and materials science, as it helps explain the diverse characteristics of elements. Other elements, like oxygen, also have allotropes, such as O2 (dioxygen) and O3 (ozone), each with unique properties and functions in nature.