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?

Theme table
 

Presentation