From 2D to 3D: Escher Drawings - Crystallography, Crystal Chemistry, and Crystal "Defects"

Peter Buseck
Arizona State University
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This activity was selected for the On the Cutting Edge Reviewed Teaching Collection

This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

  • Scientific Accuracy
  • Alignment of Learning Goals, Activities, and Assessments
  • Pedagogic Effectiveness
  • Robustness (usability and dependability of all components)
  • Completeness of the ActivitySheet web page

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This page first made public: Aug 19, 2008


This set of exercises illustrates plane and space groups as well as crystal chemistry and "defects" in crystals. The problems are designed to present the material as puzzles that are visually attractive and intellectually challenging.

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This exercise is designed for a sophomore or junior level required course in mineralogy.

Skills and concepts that students must have mastered

Students should have a basic familiarity with symmetry elements, unit cells (2D and maybe 3D), and have been exposed to the concepts of plane groups.

How the activity is situated in the course

This is a stand-alone exercise.


Content/concepts goals for this activity

This exercise was designed to increase students' skills in understanding mineral symmetry, unit cells, plane and space groups, crystal chemistry, and "defects" in crystals.

Higher order thinking skills goals for this activity

Other skills goals for this activity

Description of the activity/assignment

This problem set uses Escher drawings as 3-D projections to make analogies to real minerals as well as order/disorder relations to provide examples of features found in real minerals (e.g. superstructures, substitutions, structural defects, and modulated and incommensurate structures).

Determining whether students have met the goals

Students have met the goals of this activity if they answer the problem set completely and accurately.

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