MIRROR PLANE

Last Update 29/ 08/ 2003

in English/ in Esperanto/ in Portuguese

When this page is uploaded or after a click on button a, the incipient student of crystallography and related disciplines may not recognize the unique symmetry element on this chair. But after a click on button b the foremost part of the chair related to the mirror plane is displayed. The short notation for this plane is m (from mirror) according to the notation of Hermann-Maugin or S (from Spiegel) if Schoenflies' notation is adopted. Due to the lack of symmetry this part of the chair is named an asymmetric unit.
The other asymmetric unit can be observed after a click on button c. After a click on button d the chair is oriented along the orthogonal base with the origin at point 0. Table 1 shows the coordinates of two chair corners located just in front and behind the mirror plane.

Table 1 Coordinates of two chair corners.
Point location coord. x coord. y coord.z cursor's x  cursor's y
in front of m -1 1 0 118 139
behind  -1 0 0 78 99

When the cursor on the computer video exhibits the coordinates x = 118 and y = 139, the coordinates on the orthogonal base are x = -1.0; y = 1.0 and z = 0.0 (in arbitrary units, au). The distance of this point to the mirror plane is 0.5 au. In a similar way, the reflected point with cursor coordinates x = 78 and y = 99 for the point with base coordinates x = -1.0; y = 0.0 and z = 0.0 is located 0.5 au behind the mirror plane. These two points are equivalent, equidistant and opposed (on the same normal line) to the mirror plane. Only one half of the points of the chair are enough to define it, the other half may be obtained by the symmetry operation defined by the reflection plane.

Exercises for more advanced students

1) Justify why the above mentioned mirror plane may be defined by the Miller indices (0 2 0).

2) Would there be any advantage to set the origin of the orthogonal base coincident with the mirror plane?

Please send your comments.

Table of subjects.
Presentation
Chemistry Analytical Chromatography
Elemental organic analysis
Volumetric analysis, simulation
Crystallography 3 fold screw axis
4 fold inversion axis on tetrahedron
5 fold rotation axis absent in crystallography
Binary axis and reflection plane in stereographic projection
Bravais lattices
Conic sections under symmetry operators
Converting from spherical coordinates to stereographic projection
Crystal lattice and unit cell
Determination of unit cell
Elements of symmetry in action - animation
Elements of symmetry in action - cube game
Elements of symmetry in action - dodecahedron game
Elements of symmetry in action - icosahedron game
Elements of symmetry in action - octahedron game
Elements of symmetry in action - tetrahedron game
Ewald sphere and crystal measurements
Extinctions
Five classes in the cubic system
Five classes in the rhombohedral system
From tetrahedron to prism
Gnomonic projection
Improper symmetry axis
Miller indices
Miller indices - animation
Miller indices - cube game
Miller indices - octahedron game
Miller indices - rhombic dodecahedron game
Miller indices - tetrahedron game
Mirror plane
Orientations of the cube
Plane symmetry groups
Question on point group
Rotation axis in octahedron and Werner compounds
Rotation axis on tetrahedron and organic molecules
Rotation of the parallel and stereographic projections of the cube
Seven faces in stereographic projection
Seven classes in the hexagonal system
Seven classes in the tetragonal system
Six elements of symmetry in seven orientations
Spherical projection of the octahedron
Stereographic projection
Stereographic projection of six polyhedra in different orientations
Straight line equations and symmetry elements
Symmetry, 2 fold axis
Symmetry, 2, 3 and 6 fold axis in benzene
Symmetry, 3 fold axis in the cube
Symmetry, 4 fold axis in the cube
Symmetry, 4 fold axis in the unit cell of gold
Symmetry elements and Miller indices game
Symmetry elements and Miller indices game - octahedron
Symmetry in art and in crystallography
Three classes in the monoclinic system
Three classes in the orthorhombic system
Twin crystals
Two classes in the triclinic system
Unit cell in hexagonal net
General Butane conformations
Density
Electrochemical cell
Ethane conformations
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold