Trihexagonal tiling

Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines.

[2] This pattern, and its place in the classification of uniform tilings, was already known to Johannes Kepler in his 1619 book Harmonices Mundi.

[4] Kagome (Japanese: 籠目) is a traditional Japanese woven bamboo pattern; its name is composed from the words kago, meaning "basket", and me, meaning "eye(s)", referring to the pattern of holes in a woven basket.

In 2022, archaeologists found bamboo weaving remains at the Dongsunba ruins in Chongqing, China, 200 BC.

The term kagome lattice was coined by Japanese physicist Kôdi Husimi, and first appeared in a 1951 paper by his assistant Ichirō Shōji.

Some minerals, namely jarosites and herbertsmithite, contain two-dimensional layers or three-dimensional kagome lattice arrangement of atoms in their crystal structure.

[14] The term is much in use nowadays in the scientific literature, especially by theorists studying the magnetic properties of a theoretical kagome lattice.

[1] The second is called a cantic hexagonal tiling, h2{6,3}, with two colors of triangles, existing in p3m1 (*333) symmetry.

Edges have p vertices arranged like a regular polygon, and vertex figures are r-gonal.