This is the summary of a presentation given at the Joint Mathematics
Meetings, January 1013, 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 starlike
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
