Icosanoic acid

Icosahedral symmetry is a type of symmetry that is commonly found in mathematics, particularly in geometry, and in the natural world. It is one of the types of point group symmetries in three dimensions.

Definition

The term "icosahedral symmetry" refers to the symmetry of an icosahedron, a polyhedron with 20 faces. This symmetry is characterized by 60 rotational or orientation-preserving symmetries, and 120 symmetries if reflections are included. These symmetries form a group known as the icosahedral group, which is a subgroup of the octahedral group.

Mathematical Properties

In mathematical terms, icosahedral symmetry is represented by the Coxeter notation H3, and Schläfli symbol {3,5}. The icosahedral group is one of the 7 finite Coxeter groups, which are important in the study of regular polytopes and Euclidean geometry.

In Nature

Icosahedral symmetry is also found in nature, particularly in the structure of many viruses. These viruses, including the HIV and hepatitis B virus, have an icosahedral capsid, a protein shell that encloses the viral genome. This structure allows for a high degree of efficiency in packing the viral genome.

In Art and Architecture

Icosahedral symmetry is also found in art and architecture, particularly in the design of geodesic domes, which were popularized by architect Buckminster Fuller. These structures, which are composed of triangular elements arranged in an icosahedral pattern, are known for their strength and efficiency.

See Also

• Symmetry in biology
• Symmetry in physics
• Symmetry in chemistry
• Symmetry in mathematics