% Qualitative report-plane schematic only; radii and phases are not data. % Inner phases: cube roots of unity. Outer phases: two conjugate pairs with % cosines x=3/5 and y=-5/6 (xy=-1/2), an illustrative member of the % construction of eq:sevenphases; the actual x,y follow from the certified branch. \begin{tikzpicture}[font=\small,>=stealth,line cap=round] \definecolor{innerblue}{HTML}{0072B2} \definecolor{outerorange}{HTML}{D55E00} \draw[->,gray] (-2.15,0) -- (2.3,0) node[right,black] {\(a_1\)}; \draw[->,gray] (0,-2.1) -- (0,2.15) node[above,black] {\(a_2\)}; \draw[innerblue,densely dashed] (0,0) circle (.85); \draw[outerorange] (0,0) circle (1.7); \draw[innerblue!60,densely dotted] (0:.85) -- (120:.85) -- (240:.85) -- cycle; \draw[outerorange!60,densely dotted] (53.13:1.7) -- (-53.13:1.7); \draw[outerorange!60,densely dotted] (146.44:1.7) -- (-146.44:1.7); \draw[->,innerblue] (0,0) -- (60:.85) node[pos=.55,right,black] {\(r_-\)}; \draw[->,outerorange] (0,0) -- (-100:1.7) node[pos=.82,left,black] {\(r_+\)}; \foreach \a in {0,120,240} \fill[innerblue] (\a:.85) circle (2.8pt); \foreach \a in {53.13,-53.13,146.44,-146.44} \node[draw=outerorange,line width=.9pt,fill=white,inner sep=2.4pt] at (\a:1.7) {}; \node[anchor=west,align=left] at (2.75,.75) {\textcolor{innerblue}{\(\bullet\)} Inner triple at the cube roots of unity,\\ \phantom{\(\bullet\)} equal weights}; \node[anchor=west,align=left] at (2.75,-.55) {\textcolor{outerorange}{\(\square\)} Outer four: two complex-conjugate pairs\\ \phantom{\(\square\)} whose phases \(w\) have \(\mathrm{Re}\,w=x,y\) of Eq.~\eqref{eq:sevenphases}}; \end{tikzpicture}