A kagome lattice is an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points. Although called a lattice, it is more closely related to the trihexagonal tiling than to a mathematical lattice.
Its name derives from two separate Japanese words, meaning the pattern of holes ("me", literally "eyes") in a basket ("kago"). There has been some debate about the proper way to write this term. Lately, it is understood that it is not strictly a Japanese word in itself and it is not the name of a person. Hence, it is proper for kagome to be written in roman font, not italic (foreign words), with a lower-case k, and without an unnecessary (pronunciation) acute accent on the last e.
Some minerals, namely jarosites and herbertsmithite, contain layers with kagome lattice arrangement of atoms in their crystal structure. These minerals display novel physical properties connected with geometrically frustrated magnetism. The term is much in use nowadays in the scientific literature, especially by theorists studying the magnetic properties of a theoretical kagome lattice in two or three dimensions.
The term was first coined by Japanese physicist Kōji Fushimi, who was working with Ichirō Shōji. The first paper[1] on the subject appeared in 1951. There is an article [2] in Physics Today about all this.