**Example 5.15.14**
Let

be the group

with generators
given to be the set of all transpositions:

(There are many more transpositions than necessary to generate

since the subset of transpositions of the form

,

,
suffice to generate

[

R].) The algorithm
of Steinhaus (see §

4.5) shows that
there is a Hamiltonian circuit in the Cayley graph of

with respect to

.

**Exercise 5.15.15**
Find the Cayley graph of the

**sliced squared group**
where

is the middle slice move which turns the middle slice
parallel to the right face clockwise 90 degrees (with respect
to the right face). Find the diameter of this graph.