24 Jun 2013

Lattice Systems Origami

In-Class Activity

Submitted by Jeremiah Duncan, Plymouth State University

Covers the geometries and symmetries of the seven crystal systems in an inquiry-based manner. 2-D paper templates are provided, which the students cut out, fold, and tape together to create 3-D representations of the seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic. The students can then use these to determine the geometries and symmetries of the systems for themselves.

Learning Goals: 

In this activity, a student will:

  1. Determine the geometries of the seven crystal systems.
  2. Identify the following symmetry elements in a 3-D system: rotational axis and mirror planes.


Equipment needs: 

printouts of the templates


tape (recommended) or glue

Evaluation Methods: 

Through the course of the exercise, students populate a table with the geometries and symmetry elements of each crystal system. The instructor can review these tables with students in class. In addition, templates without labels have been provided that can be used to quiz students.

Evaluation Results: 

I have not formally assessed this activity, though I used it once to introduce crystal systems to my Junior/Senior level Inorganic chemistry course. The activity was well received; students took their 3-D paper models home, and some later told me they saved them and used them to study for the exam. I will teach this class again in Spring 2014, at which time I will more formally assess the activity.

Creative Commons License: 
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