Add Cayley diagram for A4

[dcernst]

I have some code for a planar version on Fall 2020 Final Exam. Here is some code for a truncated tetrahedron from Matt Macauley.

\begin{figure}[!ht] \tikzstyle{v-small} = [circle, draw, fill=lightgrey,inner sep=0pt, minimum size=5.5mm] \tikzstyle{v-tiny} = [circle, draw, fill=lightgrey,inner sep=0pt, minimum size=5mm] \tikzstyle{v-faded} = [circle, draw, grey, fill=lightgrey,inner sep=0pt, minimum size=5mm] \tikzstyle{bb-faded} = [draw, thick, lightblue] \tikzstyle{r-faded} = [draw, thick, lightred, -stealth] \begin{tikzpicture}[scale=1,auto] \begin{scope}[shift={(0,0)},scale=1.95] \node (l1) at (-.05,.8) [v-tiny] {\footnotesize $x$}; \node (l2) at (0,.4) [v-tiny] {\footnotesize $b$}; \node (l3) at (.5,0) [v-tiny] {\footnotesize $c^2$}; \node (t1) at (.85,2.5) [v-tiny] {\footnotesize $e$}; \node (t2) at (1.3,2.8) [v-tiny] {\footnotesize $a^2$}; \node (t3) at (1.8,2.55) [v-tiny] {\footnotesize $a$}; \node (r1) at (2.4,.2) [v-tiny] {\footnotesize $d^2$}; \node (r2) at (2.5,.7) [v-faded] {\footnotesize\color{darkgrey} $z$}; \node (r3) at (2.9,.9) [v-tiny] {\footnotesize $c$}; \node (m2) at (1.15,1.9) [v-faded] {\footnotesize\color{darkgrey} $b^2$}; \node (m1) at (.8,1.25) [v-faded] {\footnotesize\color{darkgrey} $d$}; \node (m3) at (1.5,1.3) [v-faded] {\footnotesize\color{darkgrey} $y$}; \draw [r-faded] (r1) to (r2); \draw [r-faded] (r2) to (r3); \draw [bb-faded] (l2) to (m1); \draw [bb-faded] (m2) to (t2); \draw [bb-faded] (r2) to (m3); \draw [r-faded] (m1) to (m2); \draw [r-faded] (m2) to (m3); \draw [r-faded] (m3) to (m1); \draw [bb] (l1) to (t1); \draw [bb] (l3) to (r1); \draw [bb] (r3) to (t3); \draw [r] (l1) to (l2); \draw [r] (l2) to (l3); \draw [r] (l3) to (l1); \draw [r] (t1) to (t3); \draw [r] (t2) to (t1); \draw [r] (t3) to (t2); \draw [r] (r3) to (r1); \node at (0,-.2) {}; \end{scope} %% \begin{scope}[shift={(11,2)},scale=.8] \node (l1) at (0,2.25) [v-small] {\small $x$}; \node (l2) at (-.866,3.75) [v-small] {\small $b$}; \node (l3) at (.866,3.75) [v-small] {\small $c^2$}; \node (t1) at (0,1) [v-small] {\small $e$}; \node (t2) at (-.866,-.5) [v-small] {\small $a^2$}; \node (t3) at (.866,-.5) [v-small] {\small $a$}; \node (r1) at (3.68,-1.125) [v-small] {\small $d^2$}; \node (r2) at (2.814,-2.5) [v-small] {\small $z$}; \node (r3) at (1.948,-1.125) [v-small] {\small $c$}; \node (m2) at (-1.948,-1.125) [v-small] {\small $b^2$}; \node (m1) at (-3.68,-1.125) [v-small] {\small $d$}; \node (m3) at (-2.814,-2.5) [v-small] {\small $y$}; \draw [bb] (l2) to (m1); \draw [bb] (m2) to (t2); \draw [bb] (r2) to (m3); \draw [bb] (l1) to (t1); \draw [bb] (l3) to (r1); \draw [bb] (r3) to (t3); \draw [r] (l1) to (l2); \draw [r] (l2) to (l3); \draw [r] (l3) to (l1); \draw [r] (t1) to (t3); \draw [r] (t2) to (t1); \draw [r] (t3) to (t2); \draw [r] (r1) to (r2); \draw [r] (r2) to (r3); \draw [r] (r3) to (r1); \draw [r] (m1) to (m2); \draw [r] (m2) to (m3); \draw [r] (m3) to (m1); \node at (0,-.2) {}; \end{scope} \end{tikzpicture} \caption{The Cayley diagram for $A_4=\<a,x>$ can be laid out on a truncated tetrahedron. Here, $a$ and $x$ can be taken to be $(123)$ and $(12)(34)$, respectively.}\label{fig2:A4-Cayley} \end{figure}

[dcernst]

And more from my grad notes.

[dcernst]

I included some Cayley diagrams for A_4, but it might be nice to include a 3-D version of one. The code above will need to be tweaked in order to match the existing Cayley diagrams in book.