Watch the video "Three-dimensional Symmetry".
Learn from the video about the four kinds of symmetry for figures in the plane and in space:
and the two additional kinds of symmetry for figures in space:
At home, read the handout on symmetries in the plane.
Each student group makes the two polyhedra listed below out of Polydrons (the solid polygon pieces).
| Group 0 | 3.3.3.3.3 | 3.3.6 |
| Group 1 | 5.6.6 | 3.3.3 |
| Group 2 | 3.5.3.5 | 4.4.4 |
| Group 3 | 5.5.5 | 3.8.8 |
| Group 4 | 3.4.4.4 | 3.3.5 |
For each polyhedron determine and mark all the planes of reflection symmetry. Mark them by running a strip of tape around the polyhedron where the mirror would cut the polyhedron. That is, if you cut along the taped lines, you would cut the polyhedron into halves which are mirror images of each other.
For each polyhedron determine and mark
Mark the points where the axes of rotation would puncture the polyhedron with stick-on dots, and write the "order" of the rotation on the dot. (The order of a rotation is the number of times you have to repeat it to get back to the original position. For example, the order of a 5-fold rotation is 5.) Note that the dots will come in pairs, on opposite sides of the polyhedron.
Make a table showing: name/vertex type of polyhedron number of planes of reflection symmetry number of axes of 2-fold rotation symmetry number of axes of 3-fold rotation symmetry, etc.
Combine your information with that of the rest of the class---discussion next time. But think about this question: what is a good way to sort all the polyhedra we made in this and previous activities into categories?
Store your marked polyhedra in JB 368 at the end of class.
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