*OD Explorer* is a "virtual laboratory" for the analysis of Order/Disorder (OD) structures.
The OD theory was developed in the 1950s to explain unusual diffraction phenomena
and disorder in minerals like wollastonite
and isotypic inorganic compounds like Madrell's salt (NaPO_{3}) and the isotypic sodium polymetaarsenate.
The arguments of OD theory apply to all classes of compounds and it has been fruitfully
applied to minerals, synthetic inorganic compounds, organic compounds and even
biological macro-molecules.

OD theory is based on the geometric equivalence
of pairs of layers. A structure is said to fulfill the *vicinity condition* (VC) if

- It is composed of a finite number of kinds of layers periodic in two dimensions
- Adjacent pairs of layers share a common two dimensional lattice
- Equivalent sides of a layer can connect to other layers only in such a way that the resulting pairs of layers are equivalent

Structures which fulfill the VC and allow for different stacking possibilities
are said to be *proper OD structures*, otherwise *fully ordered structures*.
All resulting stacking possibilities belong to an OD family. If interatomic interactions of atoms distanced
by more than a layer width are neglected, all members of an OD family are energetically equivalent,
thus leading to polytypism.

For more details on OD theory see:

- MaThCryst page on OD structures
- On the theory of order-disorder (OD) structures
Acta Cryst.
**14**, 167-177 (1961) - Zur Symmetriebeschreibung von OD-Kristallstrukturen durch Brandtsche und Ehresmannsche Gruppoide
Beiträge zur Algebra und Geometrie
**6**, 71-99 (1977)

Inspired by the Superspace Group Finder, we decided to provide similar functionality for OD groupoid families. The aim of the project is twofold:

- Provide crystallographers a tool to analyze OD families. Since there are an infinity of OD families,
it will never be possible to publish an equivalent to the
*International Tables of Crystallography Vol. A*. Help in preparation of graphics and symbols for publication. - Provide a code base which enables the testing of conjectures and thus the advancement of OD theory (
*i.e.*a "virtual lab").

*OD Explorer* is alpha-level software in development. So far only rudimentary features have been implemented
and the software is practically untested.

A list of design decision which will or will not be met and may or may not be useful. Time will tell.

- All algorithms are purely symbolic. No floating point operations are used.
- Allow lazy input.
*E.g.*the user may input the layer group*pmm*(1) instead of*pmm*(2), since the 2-operation is implicitely generated by the*m*operations. - Allow multiple ways of input.
*E.g.*the inverse function of cotan may be input as acot, acotan, arccot or arccotan. - Code readability over speed
- Correctness over speed
- Input and output Unicode (UTF-8 encoding). Notably greek characters, squareroot sign, mathematical signs.

Usage at the moment is very simple: The user inputs the symbol of an OD family. The software outputs a number of statistics. At the moment special parameters and the corresponding stacking possibilities are listed.