Chemical conformation and cyclohexane

22 Definition (Chirotope) An alternating, not constantly zero function n — +,0 fulfUlingthe binary Grassmann-Plucker relations 

the orientation function of any sequence of atoms that are not all in one plane is a chirotope. The orientation function of a sequence of n spanning points in d-dimensional Euclidean space is a chirotope of rank k = d + l. The chirotope is said to be uniform if and only if the sequence of points is in general position, i.e. if each (d -i- l)-subset is affinely independent (i.e. linearly independent). If the points are not spanning, then the orientation function is the zero function. The realizable chirotopes correspond to the 3D point conhgurations of six atoms. We proceed as follows  

Assuming that any 4 atoms are affinely independent, we restrict the candidates to uniform chirotopes, i.e. the chirotope has no zero function values. Note that this is not a severe restriction, as one can enforce general position of the atoms by inhnitesimally small movements. 

In order to reduce the number of chirotopes that have to be considered, we prescribe a list of forbidden Radon partitions reflecting mathematical and chemical knowledge. 

Repeating the generation up to negation leads to three orientation patterns, reflecting the eneuitiomorphism of the twist forms. 

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