\newcommand{\rad}{2}

\newcommand{\upsidedown}[1]{\begin{scope}[y=-1cm] #1 \end{scope}}

\newcommand{\drawS}[3]{%
	\filldraw[fill=white,thick] (#1,#2) ellipse (3mm and 3mm);
	\node at (#1,#2) {\Large $S$};
	\path(#1,#2) ++(#3:0.37) node {$\star$};
}

\newcommand{\drawJW}[3]{%
	\filldraw[fill=white,thick] (#2,-0.2) rectangle (#3,0.2);
	\node at (#2/2+#3/2,0) {\Large$\JW{#1}$};
}

\newcommand{\RainbowOne}{
	\fill[shaded] (-0.8,0) -- (-0.8,0.6) arc (180:0:0.8) -- (0.8,0) -- (0.2,0) -- (0.2,1) -- (-0.2,1) -- (-0.2,0);
	\draw (-0.8,0) -- (-0.8,0.6) arc (180:0:0.8) -- (0.8,0);
	\draw (-0.2,0) -- (-0.2,1);
	\draw (0.2,0) -- (0.2,1);
%	\node at (-0.3,0.5) {$1$};
	\node at (0.45,0.5) {\footnotesize$2n-1$};
	\drawS{0}{1}{-90}
}

\newcommand{\RainbowTwo}{
	\draw (0,0) -- (0,1);
	\node at (0.15,0.5) {\footnotesize$2n$};
	\drawS{0}{1}{180}
	%\draw (-1,0) -- (-1,0.5) arc (180:0:1) -- (1,0);
	%\draw (-0.9,0) -- (-0.9,0.5) arc (180:0:0.9) -- (0.9,0);
	\filldraw[shaded] (-1,0) -- (-1,0.5) arc (180:0:1) -- (1,0)  -- (0.9,0) -- (0.9,0.5) arc (0:180:0.9) -- (-0.9,0);
}

\newcommand{\JWPlusTwo}{%
	\filldraw[fill=white,thick] (-1,-0.2) rectangle (1,0.2);
	\node at (0,0) {\Large$\JW{2n+2}$};
}

\newcommand{\JWPlusFour}{%
	\filldraw[fill=white,thick] (-1.2,-0.2) rectangle (1.2,0.2);
	\node at (0,0) {\Large$\JW{2n+4}$};
}

\newcommand{\JWwide}[1]{%
	\filldraw[fill=white,thick] (-1.2,-0.2) rectangle (1.2,0.2);
	\node at (0,0) {\Large$\JW{#1}$};
}

\newcommand{\JWFour}{%
	\drawJW{4}{-0.4}{0.4}
}


\newcommand{\STrainOneOne}{%
	\foreach \x in {-1,0} {
		\node[anchor=south] at (\x+0.5,1) {\footnotesize$n-1$};
		\draw (\x,1) -- (\x + 1, 1);
	}
	\foreach \x in {-1,0,1} {
		\drawS{\x}{1}{90}
	}
}

\newcommand{\STrainOneStrings}{%
	\fill[shaded] (-0.5,0) rectangle (0.5,1);
	\foreach \x in {-0.5,0.5} {
		\draw (\x,1) -- (\x,0);
		\node at (\x+0.25,0.5) {\footnotesize$n+1$};
	}
}

\newcommand{\STrainStrings}[2]{%
	\fill[shaded] (-0.5,0) rectangle (0.5,1);
	\draw (-0.5,1) -- (-0.5,0);
	\node[anchor=west] at (-0.5,0.5) {\footnotesize#1};
	\draw (0.5,1) -- (0.5,0);
	\node[anchor=west] at (0.5,0.5) {\footnotesize#2};
}

\newcommand{\STrainTwoStrings}{%
	\foreach \x in {-0.5,0.5} {
		\draw (\x,1) -- (\x,0);
		\node at (\x+0.25,0.5) {$n+2$};
	}
}

\newcommand{\STrainTwoRightStrings}{%
	\draw (-0.5,1) -- (-0.5,0);
	\node at (-0.25,0.5) {$n+1$};
	\draw (0.5,1) -- (0.5,0);
	\node at (0.75,0.5) {$n+2$};
	
	\draw (-0.5,1) .. controls (0.5,2) and (1,2.5) .. (1,0);
}

\newcommand{\STrainTwoLeftStrings}{%
	\draw (-0.5,1) -- (-0.5,0);
	\node at (-0.25,0.5) {$n+2$};
	\draw (0.5,1) -- (0.5,0);
	\node at (0.75,0.5) {$n+1$};
	
	\draw (0.5,1) .. controls (-0.5,2) and (-1,2.5) .. (-1,0);
}

\newcommand{\STrainOne}{%
	\node[anchor=south] at (0,1) {\footnotesize$n-1$};
	\draw (-0.5,1) -- (0.5, 1);
	\foreach \x in {-0.5,0.5} {
		\drawS{\x}{1}{90}
	}
}

\newcommand{\STrainOver}{%
        \draw (0.5,1) .. controls (-0.2,1.7) and (-1,1.7)..              
              (-1,1) .. controls (-1,0.5) and (-0.7,0.5) ..  (-0.7,0.2);
        \node at (-1.1,1) {\footnotesize$2$};
}


\newcommand{\STrainTwo}{%
	\node at (0,1.2) {$n-2$};
	\draw (-0.5,1) -- (0.5, 1);
	\foreach \x in {-0.5,0.5} {
		\drawS{\x}{1}{90}
	}
}

\newcommand{\STrainOneOneStrings}{%
	\fill[shaded] (-1,1) rectangle (1,0);
	\foreach \x in {-1,0,1} {
		\draw (\x,0) -- (\x,1);
	}
	\foreach \x in {-1,1} {
		\node at (\x + 0.2,0.5) {\footnotesize$n+1$};
	}
	\node at (0.1,0.5) {\footnotesize$2$};
}

\newcommand{\STrainThreeStrings}[3]{%
	\fill[shaded] (-1,1) rectangle (1,0);
	\foreach \x in {-1,0,1} {
		\draw (\x,0) -- (\x,1);
	}
        \node [anchor=west] at (-1,0.5) {\footnotesize#1};
        \node [anchor=west] at (0,0.5) {\footnotesize#2};
	\node [anchor=west] at (1,0.5) {\footnotesize#3};
}