Glide mirror

Figure 8-3. Illustrations for glide mirrors, (a) Pillow-edge from Buzsak, Hungary (used with permission from Gyorgyi Lengyel) (b) Function describing simple harmonic motion (reflection occurs following translation along the t axis by half a period, 772).

Figure 8-2. Canons illustrating repetition (a) and repetition combined with reflection (glide-mirror symmetry) (b).

There is an international notation (lUC, International Union of Crystallography) which describes the pattern properties such as m (mirror), g (gliding mirror), pi... 

Figure 40. Convergent beam electron diffraction pattern exhibiting Gj0nnes-Moodie lines due to the presence of glide mirror planes and twofold screw axis [1681...

These include rotation axes of orders two, tliree, four and six and mirror planes. They also include screM/ axes, in which a rotation operation is combined witii a translation parallel to the rotation axis in such a way that repeated application becomes a translation of the lattice, and glide planes, where a mirror reflection is combined with a translation parallel to the plane of half of a lattice translation. Each space group has a general position in which the tln-ee position coordinates, x, y and z, are independent, and most also have special positions, in which one or more coordinates are either fixed or constrained to be linear fimctions of other coordinates. The properties of the space groups are tabulated in the International Tables for Crystallography vol A [21]. 

Orthorhombic symmetry mm2 comprises two mirror planes perpendicular to each other, which automatically generates a twofold axis along the line of intersection. This point symmetry applies to all noncentrosymmetric orthorhombic crystals that have mirror or glide planes such as those of space groups Pna2t and Pca2,. 

In an infinite Fischer projection, chirality is not consistent with the presence of the following elements of reflective synunetry (41, 46, 254) d, mirror plane containing the chain axis m, an infinite number of mirror planes perpendicular to the chain axis and/or c, mirror glide plane containing the chain axis. For... 

The elements of mirror symmetry d, m, and c can be removed in different ways, resulting in different classes of chiral polymers. Plane d containing the polymer chain is eliminated by the presence, in the main chain, of tertiary carbon atoms —CHR—), or of quaternary atoms with different substituents (—CR R"—), or with equal chiral substituents (—CR R —). Mirror glide plane c does not exist in isotactic structures, nor in syndiotactic ones in which the substituents are chiral and of the same configuration, 75 (33, 263). The perpendicular planes, m, are eliminated by the presence of chiral substituents of the same sign in syndiotactic, 75 (33, 263) or isotactic structures, 76 (263) or if the two directions of the chain are rendered nonreflective. This last condition can be realized in different ways some of which follow (264) ... 

Inversion centre Mirror plane Glide plane... 

Same as mirror plan, but followed by a translation of half the unit cell parallel to the plane glide planes are not relevant in macromolecular crystallography due to the chirality of the biological building blocks... 

The stereocenters in all three stereoregular polymers are achirotopic. The polymers are achiral and do not possess optical activity. The diisotactic polymers contain mirror planes perpendicular to the polymer chain axis. The disyndiotactic polymer has a mirror glide plane of symmetry. The latter refers to superposition of the disyndiotactic structure with its mirror image after one performs a glide operation. A glide operation involves movement of one structure relative to the other by sliding one polymer chain axis parallel to the other chain axis. 

All four diisotactic polymers (cis and trans, erythro and threo) are chiral and possess optical activity. Each of the four disyndiotactic polymers possesses a mirror glide plane and is achiral. For symmetric 1,4-disubstituted 1,3-butadienes (R = R ), only the cis and transthreo-diisotactic structures are chiral. Each of the erythrodiisotactic and threodisyndiotactic polymers has a mirror glide plane. Each of the erythrodisyndiotactic polymers has a mirror glide plane. 

The symbols for plane groups, the Hermann-Mauguin symbol, have been the standard in crystallography. The first place indicates the type of lattice, p indicates primitive, and c indicates centered. The second place indicates the axial symmetry, which has only 5 possible vales, 1-, 2-, 3-, 4-, and 6-fold. For the rest, the letter m indicates a symmetry under a mirror reflection, and the letter g indicates a symmetry with respect to a glide line, that is, one-half of the unit vector translation followed by a mirror reflection. For example, the plane group pAmm means that the surface has fourfold symmetry as well as mirror reflection symmetries through both x and y axes. 

---