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Facial bilateral symmetry is typically defined as fluctuating asymmetry of the face comparing random differences in facial features of the two sides of the face. [4] The human face also has systematic, directional asymmetry : on average, the face (mouth, nose and eyes) sits systematically to the left with respect to the axis through the ears ...
Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex. This is * n 32 in orbifold notation , and [ n ,3] in Coxeter notation .
D nh is the symmetry group for a "regular" n-gonal prism and also for a "regular" n-gonal bipyramid. D nd is the symmetry group for a "regular" n-gonal antiprism, and also for a "regular" n-gonal trapezohedron. D n is the symmetry group of a partially rotated ("twisted") prism. The groups D 2 and D 2h are noteworthy in that there is no special ...
The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6]
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; [1] a three-dimensional solid bounded exclusively by faces is a polyhedron. A face can be finite like a polygon or circle, or infinite like a half-plane or plane.
In 1981, Bernhard Flury and Hans Riedwyl suggested "asymmetrical" Chernoff faces; [3] since a face has vertical symmetry (around the y axis), the left side of the face is identical to the right and is basically wasted space – a point also made by Tufte. [4]
A regular polyhedron is identified by its Schläfli symbol of the form {n, m}, where n is the number of sides of each face and m the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids ), and four regular star polyhedra (the Kepler–Poinsot polyhedra ), making nine regular polyhedra in all.
The symbol of a space group is defined by combining the uppercase letter describing the lattice type with symbols specifying the symmetry elements. The symmetry elements are ordered the same way as in the symbol of corresponding point group (the group that is obtained if one removes all translational components from the space group).