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Aurofacial asymmetry (from Latin auris 'ear' and facies 'face') is an example of directed asymmetry of the face. It refers to the left-sided offset of the face (i.e. eyes, nose, and mouth) with respect to the ears. On average, the face's offset is slightly to the left, meaning that the right side of the face appears larger than the left side.
This example shows Chernoff faces for lawyers' ratings of twelve judges. Chernoff faces, invented by applied mathematician, statistician, and physicist Herman Chernoff in 1973, display multivariate data in the shape of a human face. The individual parts, such as eyes, ears, mouth, and nose represent values of the variables by their shape, size ...
Fluctuating asymmetry (FA) is often considered to be the product of developmental stress and instability, caused by both genetic and environmental stressors. The notion that FA is a result of genetic and environmental factors is supported by Waddington's notion of canalisation, which implies that FA is a measure of the genome's ability to successfully buffer development to achieve a normal ...
Facial symmetry has been shown to be considered attractive in women, [186] [187] and men have been found to prefer full lips, [188] high forehead, broad face, small chin, small nose, short and narrow jaw, high cheekbones, [39] [189] clear and smooth skin, and wide-set eyes. [64]
Examples include Circoporus octahedrus, Circogonia icosahedra, Lithocubus geometricus and Circorrhegma dodecahedra; the shapes of these creatures are indicated by their names. [5] The outer protein shells of many viruses form regular polyhedra. For example, HIV is enclosed in a regular icosahedron, as is the head of a typical myovirus. [6] [7]
Symmetry in physics has been generalized to mean invariance—that is, lack of change—under any kind of transformation, for example arbitrary coordinate transformations. [17] This concept has become one of the most powerful tools of theoretical physics , as it has become evident that practically all laws of nature originate in symmetries.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
An icosahedron and related symmetry polyhedra can be used to define a high geodesic polyhedron by dividing triangular faces into smaller triangles, and projecting all the new vertices onto a sphere. Higher order polygonal faces can be divided into triangles by adding new vertices centered on each face.