Department of Natural Sciences The Hebrew University of Jerusalem The Open University of Israel Shoham - The Center for Technology in Distance Education home page Continuous Symmetry Measures


Measuring the degree of symmetry, of chirality, and of polyhedral shapes

How far is a given molecule from having rotational symmetry?
By how much is one molecule more chiral than the other?
How much of perfect tetrahedricity is there in a distorted tetrahedron?

This website provides straightforward answers to these and many other related questions: A number, on a scale from zero to 100, describes the distance of a given structure from perfect symmetry; or how much chirality it contains; or to what extent it resembles a polyhedron. The approach to all of these questions is based on the same general principle. That general principle is translated into a computational method for measuring the degree of symmetry point groups, from which several additional specific important measures are derived:
  Measuring the degree of chirality
  Measuring the degree of the basic symmetry elements
  Measuring the degree of polyhedral shape content

The continous symmetry measures have been developed by the research group of Prof. David Avnir ,The Institute of Chemistry, The Hebrew University of Jerusalem, and are based on the PhD thesis of Dr. Hagit Zabrodsky Hel-Or (today at Haifa University).

This website is a joint project of the Hebrew University of Jerusalem and the Open University of Israel, and is part of the course "Analysis of Experiments" at the Open University of Israel for undergraduate chemistry students.

The Open University Team:
Dr. Inbal Tuvi-Arad - content, project manager
Dr. Dina Yogev-Einot - content, QA
Dov Garmise - Web programming
Uri Shefi - Web programming
Roy Sharoni - Web programming, html
Itai Hareven - technical consultant
Zeev Pearl - graphics
Rachel Aharon-Shriki - graphics
Yoav Breuer - Language editing (Hebrew)
Barbara Grant - Language editing (English)
Gila Haimovic - Language editing (English)

The Hebrew University Team:
Prof. David Avnir - content
Dr. Dina Yogev-Einot - content, QA
Dr. Mark Pinsky - program development
Dr. Alexander Sterkin - program development
Shadi Laham - program development
Haim Drizon - QA

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