The
following picture provides a new visual approach to
the order-8 quaternion group's
automorphisms.
Click the above image for some context.
Here
the cube is called "eightfold" because the eight vertices,
like the eight subcubes of a 2×2×2 cube,* are thought of as
independently movable. See The Eightfold Cube.
See also…
- The 1985 note from which the above figures were drawn
- Visualizing GL(2,p)
- Quaternions in an Affine
Galois Plane
Related
material: Robin Chapman and Karen E. Smith
on the quaternion group's automorphisms.
*
See Margaret Wertheim's Christmas Eve remarks on
mathematics
and the following eightfold cube from an institute she co-founded—
© 2005 The Institute for Figuring
Photo by Norman Brosterman
fom the Inventing
Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)