"The group of 8" is a phrase from politics, not mathematics.
Of the five groups of order 8 (see today's noon post),
the one pictured* in the center, Z2 × Z2 × Z2 , is of particular
interest. See The Eightfold Cube. For a connection of this
group of 8 to the last of the five pictured at noon, the
quaternion group, see Finite Geometry and Physical Space.
* The picture is of the group's cycle graph.
