My Notes
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This activity allows students to manipulate highly symmetric objects and find the symmetry elements that are present.
| Attachment | Size |
|---|---|
| Polyhedral Die Symmetry Exercise_0.docx | 19.85 KB |
A student will be able to distinguish a symmetry element from a symmetry operation.
A student will be able to identify symmetry elements that are present for an object.
A student will be able to realize that objects with the same elements share a point group.
A student will be able to identify a principal axis for symmetry analysis.
A student will be able to rationalize why Oh and Td are "cubic groups."
Polyhedral dice set(s) including a d4, d6, d8, d10, d12, and d20.
I have students work in pairs or groups of three. The beauty of this activity is that I can get out of the way and let them learn. Some students have used masking tape so that they can draw on the dice faces.
Evaluation
I do not evaluate this activity using points or a grade. Rather I bring everyone back together to have a discussion on what was present in each die, what die have the same point group, and how the d4, d6, and d8 are all "cubic."
Students often recognize that:
The d4 is the only die that lacks an i
The d6 and d8 are in the same point group
The d12 and d20 are in the same point group
The d4, d6, and d8 can be aligned along a common S4 axis
Students over complicate this activity by:
Trying to find all operations or count the total number of each element present. The latter is fine (even encouraged), the former is tedious.
Showing concern over mirror plane designation as σv vs σd vs σh. The distinction of a σh is important, the σv vs σd much less so at this time.
The d10 is the only die with one definite principal axis.