Dr. Frank Hoffmann, Dipl.-Chem. Michael Sartor, and Prof. Dr. Michael Fröba

The Fascination of Crystals and Symmetry

  • 30 Dec. 2014
  • 8 weeks
  • English
  • Chemistry

Make it count!

Certify your learning by choosing one of our certificate tracks or simply audit the course without a certificate. Whatever your learning needs are, we have the right track for you. Learn more

Certificate how

About this course

Course Summary

In this course, we will provide you with a basic introduction into crystallography. The focus is placed upon the symmetry elements, which occur in crystals. The arrangement of the atoms inside the crystal needs a more detailed description than the overall shape of the crystal (morphology). We want to show you how symmetry is classified in a hierarchical way. We want our students to gain the ability to discover symmetry on their own.

What will I learn?

At the end of the course you will be aware of the similarities between the patterns on wallpaper and the structures of crystals, be able to classify the innumerable appearances of crystals into the seven different crystal systems, know how to find crystallographic data and how to analyze it regarding symmetry, you will understand the International Tables for Crystallography and will be familiar with software for analyzing and drawing crystals structures.

What do I have to know?

Basic knowledge in chemistry (atoms, simple molecules).

Course Structure

Chapter     Topic
Chapter 1        Introduction to Crystals and Crystal Systems
Chapter 2        Crystal Systems, Fractional Coordinates, and Morphology of Crystals
Chapter 3        The World of Symmetry, Crystal classes and Plane groups
Chapter 4        Glide planes, Screw axes and Space groups
Chapter 5        Quasicrystals and Real Crystal Structures (in 3D)
Chapter 6        Metal-Organic Frameworks and Networks
Chapter 7        Practising Topology Determination, Tilings


Approx. 4 hours per week.

Choose the track that suits you!

Earn a certificate now or enrol for free. You can upgrade later.

Audit Track

  • All Course Material
  • Course Community
  • Statement of Participation
  • Flexible Upgrade

Certificate Track


Introductory Price

  • Course Community
  • Graded Online Exam
  • Certificate of Accomplishment
  • Certificate Supplement

Audit Track

Audit the course

With the Audit Track, you get free access to all the course materials, including lecture videos, assignments, and more! it is possible to download the lecture materials so you can browse the content at your own convenience, without having to worry about falling behind.

In addition, you also get access to the course forum. The forum is a thriving, global community of learners, where you can get peer-to-peer assistance from other students, and discuss the course content with the professors themselves!

Upgrade later

Once you have started your course, you may decide to increase your learning recognition. Our tracks offer you the option to upgrade to a higher certification level up to 2 weeks into the course. Just click on the Certificate tab in the course overview and choose a new track. It’s as easy as that!

Statement of Participation

Once you have completed 80% of the course material (video lectures and quizzes) you receive a free Statement of Participation. This confirms your active involvement throughout the course. The Statement of Participation will include your name, the instructors name, a description of the course and its duration.


All you need to participate is a stable internet connection! You can study anywhere, at anytime, at your own pace.

Certificate Track

Certify your learning

Want something more substantial? Want your work to be recognised as yours? Then the Certificate Track is made for you.

As with the Audit Track, you get access to all the course materials, lecture videos, assignments, and more. However, unlike the audit-only option, the Certificate Track also gives you access to an online-proctored exam at the end of the course. This graded exam gives you a chance to showcase the skills you’ve acquired.

Certificate of Accomplishment

After successfully completing the course, you receive an identity-verified Certificate of Accomplishment with your final grade, signed by the instructor. If you achieve a top 10% grade, this will be noted on your certificate. You can be sure your achievements are truly marked as yours as our certificates are all identity verified.

Certificate Supplement

In addition to your Certificate of Accomplishment, you will receive a Certificate Supplement. This contains detailed information about the course content and your learning achievements, backing up your hard work with the details employers may ask for.


All you need to participate is a laptop/desktop computer with a stable internet connection! In order to complete the online proctored exam a webcam and microphone are also required. You can study anywhere, anytime, at your own pace.
Generic coa sample
Not available

This track is no longer available for purchase.

What is a track? Learn more

What is a track? Hide

Found an exciting course that suits you? Great! Now it’s time to pick a track. Tracks are study paths that offer you different course workloads, certification options and more. Ready to have your accomplishments recognised? Whether you just want to enjoy free education, receive an officially verified certificate or earn ECTS credits, check out what your course tracks offer and decide how far you want to take your online learning experience.

Certificates FAQ

You have to choose a track in order to enrol in a course. If you want to test out the course before committing to a paid track, you can enrol with the free Audit Track and upgrade to another track later. Until the release of the last chapter, meaning the last week of the course, you have the chance to upgrade from the Audit Track to one of the paid tracks.
Yes, you will have access to exactly the same course content in all tracks. The Certificate, ECTS and Executive Tracks will include a final assignment that is not part of the Audit Track.
Unless clearly specified, most of our courses do not offer subtitles. Therefore, for you to make the most out of this course, it is crucial that you have a very good understanding of the language it is being taught in.
You can receive a refund within 14 days after your purchase. Please use the cancellation form that we sent you as an attachment with your purchase confirmation e-mail. After the initial fourteen days, you must defend your case and give a provable reason for your refund request.