## Orlando Meetings: Presentation Summary

Back to Orlando: Constructivism

This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

### Using a Visual Aid, the Stella Octangula, for the Group of Rotations of a Cube

This presentation was based on my successful teaching experience with students in my Abstract Modern Algebra course. Students were engaged in the geometric activity and observation in understanding concepts of groups. Students can easily figure the group of rotations of a tetrahedron as A4 by identifying each rotation with a permutation of four vertices. But to recognize the group of rotations of a cube as S4 is a mystery. I introduced visual aid, computer animated video, "The Stella Octangula," developed at the Visual Geometry Project. The stella octangula is a star-like solid whose faces are equilateral triangles. Each student built a stella octangula by gluing a small tetrahedron onto each face of the large one, matching one faces of the small tetrahedron with the center triangles (obtained from dividing each face of the large tetrahedron into 4 small equilateral triangles) on the large tetrahedron. This way, we can recognize the stella octangula as two large interpenetrating tetrahedra. By fitting a stella octangula into a cube, students can identify each rotation of a cube with a permutation of four vertices of one tetrahedron out of a stella octangula.

Saeja Oh Kim, University of Massachusetts at Dartmouth