# Twinning by metric merohedry

### From Online Dictionary of Crystallography

Maclage par mériédrie métrique(*Fr*). Meroedria metrica(*It*)

Twinning by metric merohedry is a special case of twinning by merohedry which occurs when:

- the lattice of the individual has accidentally a specialized metric which corresponds to a higher holohedry
- the twin operation belongs to this higher holohedry only

If H is the individual point group, D(H) the corresponding holohedry and D(L) the point group of the lattice, twinning by metric merohedry corresponds to D(L) ⊃ D(H) ⊇ H

Twinning by metric merohedry can be seen as the degeneration of twinning by reticular merohedry to twin index 1, or of twinning by pseudomerohedry to twin obliquity zero.

## Example

A monoclinic crystal of point group H = 2 with angle β = 90º has a orthorhombic lattice. It may undergo two types of twinning by merohedry:

- if the twin operation belongs to the monoclinic holohedry D(H) = 2/
*m*, twinning is the classical twinning by merohedry, also termed*twinning by syngonic merohedry*; - if the twin operation belongs to the orthorhombic holohedry D(L) =
*mmm*, twinning is by metric merohedry.

## Historical note

Friedel (1904, p. 143; 1926, p. 56-57) called metric merohedry **mériédrie d’ordre supérieur** (higher order merohedry) but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.