# Conditions for molecular dissymmetry

In my textbook, under the topic "Asymmetric and Dissymmetric Compounds", the following statement is given:

A molecule which does not possess plane of symmetry, centre of symmetry, and alternating axis of symmetry is called dissymmetric.

Why the definition didn't include the "axis of symmetry" as a condition for molecular dissymmetry?

• Because axes of symmetry are irrelevant for the question at hand. – Ivan Neretin Aug 8 '19 at 12:18
• chemistry.stackexchange.com/questions/104409/… – Ivan Neretin Aug 8 '19 at 12:48
• For the record, over a 10-year career in chemistry, I have never heard anyone use the word "dissymmetric." The proper word is "chiral." – Zhe Aug 8 '19 at 13:38
• @Zhe, Thank you for your reply. Actually, it is given in my textbook like that. I am also used to the term chiral, but not dissymmetric. – Guru Vishnu Aug 8 '19 at 13:42

A chiral compound can contain no improper axis of rotation ($$S_{n}$$), which includes planes of symmetry and inversion center. Chiral molecules are always dissymmetric (lacking $$S_{n}$$) but not always asymmetric (lacking all symmetry elements except the trivial identity). Asymmetric molecules are always chiral.
That means that a dyssymetric molecule lacks of $$S_{n}$$ axis(planes of symmetry and inversion centers) but can have $$C_{n}$$ axis of rotation. For example the following molecule is dissymetric: it does not have any plane of symmetry or inversion center but it has a $$C_{2}$$ axis of rotation(the "axis of rotation" is a synonyms of the "axis of symmetry" you mentioned in your question).