The Quaternion Group Acting on an Eightfold Cube

Finite Geometry Notes | Home | Site Map | Author |

The following picture provides a new visual approach to
the order-8 quaternion group's automorphisms.

IMAGE- The quaternion group acting on an eightfold cube

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 2011 remarks on mathematics
and the following eightfold cube from an institute she co-founded—

Froebel's third gift, the eightfold cube

Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)

Page created Jan. 4, 2012, by Steven H. Cullinane