The term kagome lattice was coined by Japanese physicist Kôdi Husimi, and first appeared in a 1951 paper by his assistant Ichirō Shōji.
The kagome lattice in this sense consists of the vertices and edges of the trihexagonal tiling.
Despite the name, these crossing points do not form a mathematical lattice.
A related three dimensional structure formed by the vertices and edges of the quarter cubic honeycomb, filling space by regular tetrahedra and truncated tetrahedra, has been called a hyper-kagome lattice. It is represented by the vertices and edges of the quarter cubic honeycomb, filling space by regular tetrahedra and truncated tetrahedra. It contains four sets of parallel planes of points and lines, each plane being a two dimensional kagome lattice. A second expression in three dimensions has parallel layers of two dimensional lattices and is called an orthorhombic-kagome lattice. The trihexagonal prismatic honeycomb represents its edges and vertices.
Some minerals, namely jarosites and herbertsmithite, contain two-dimensional layers or three-dimensional kagome lattice arrangement of atoms in their crystal structure. These minerals display novel physical properties connected with geometrically frustrated magnetism. For instance, the spin arrangement of the magnetic ions in CoVO rests in a kagome lattice which exhibits fascinating magnetic behavior at low temperatures. Quantum magnets realized on Kagome metals have been discovered to exhibit many unexpected electronic and magnetic phenomena. It is also proposed that SYK behavior can be observed in two dimensional kagome lattice with impurities.
The term is much in use nowadays in the scientific literature, especially by theorists studying the magnetic properties of a theoretical kagome lattice.
See also:  Kagome crests.