Graphene Graphene Graphene is an allotrope (form) of carbon consisting of a single layer of carbon atoms arranged in a hexagonal lattice. It is a semimetal with small overlap between the valence and the conduction bands (zero bandgap material).<ref name="10.1002/adma.201502544 p.6519-6525"></ref> It is the basic structural element of many other allotropes of carbon, such as graphite, diamond, charcoal, carbon nanotubes and fullerenes. Graphene has many uncommon properties. It is the strongest material ever tested, conducts heat and electricity efficiently, and is nearly transparent. Graphene shows a large and nonlinear diamagnetism, greater than that of graphite, and can be levitated by neodymium
Rotations and reflections in two dimensions Rot(−"φ"). Every reflection Ref("θ") is its own inverse. Composition has closure and is associative, since matrix multiplication is associative. Notice that both Ref("θ") and Rot("θ") have been represented with orthogonal matrices. These matrices all have a determinant whose absolute value is unity. Rotation matrices have a determinant of +1, and reflection matrices have a determinant of −1. The set of all orthogonal two-dimensional matrices together with matrix multiplication form the orthogonal group: "O"(2). Rotations and reflections in two dimensions In geometry, two-dimensional rotations and reflections are two kinds of Euclidean plane isometries which are related to one another. A rotation