%%%%% POINT %%%%%
\begin{tikzpicture}
\coordinate (point) at (0,0);
\draw[color=white,fill=white] (point) circle (.5in);
\draw[color=nred,fill=nred] (point) circle (2pt);
\node[color=nred] at (0,-.5in) {$\O_{(3)}$};
\end{tikzpicture}
\qquad
%
%%%%% UPSIDE DOWN SIMPLEX %%%%%
\begin{tikzpicture}%
	[edge/.style={color=dblue},
	facet/.style={fill=dblue,fill opacity=0.300000}]

%% Drawing the interior
%%
\fill[facet] (-0.86603, 1) -- (0.00000, -.5) -- (0.86603, 1) -- cycle {};

%% Drawing edges
%%
\draw[edge] (0.00000, -.5) -- (0.86603,1);
\draw[edge] (0.00000, -.5) -- (-0.86603, 1);
\draw[edge] (0.86603, 1) -- (-0.86603, 1);

\node[color=dblue] at (0,-.5in) {$\O_{(2,1)}$};
\end{tikzpicture}
\qquad
%
%%%%% SIMPLEX %%%%%
\begin{tikzpicture}%
	[edge/.style={color=ngreen},
	facet/.style={fill=ngreen,fill opacity=0.300000}]

%% Coordinate of the vertices:
%%
\coordinate (0.00000, 1.00000) at (0.00000, 1.00000);
\coordinate (0.86603, -0.50000) at (0.86603, -0.50000);
\coordinate (-0.86603, -0.50000) at (-0.86603, -0.50000);

%% Drawing the interior
%%
\fill[facet] (-0.86603, -0.50000) -- (0.00000, 1.00000) -- (0.86603, -0.50000) -- cycle {};

%% Drawing edges
%%
\draw[edge] (0.00000, 1.00000) -- (0.86603, -0.50000);
\draw[edge] (0.00000, 1.00000) -- (-0.86603, -0.50000);
\draw[edge] (0.86603, -0.50000) -- (-0.86603, -0.50000);

\node[color=ngreen] at (0,-.5in) {$\O_{(1,2)}$};
\end{tikzpicture}
\qquad
%
%%%%% PERMUTAHEDRON %%%%%
\begin{tikzpicture}%
	[edge/.style={color=norange},
	facet/.style={fill=norange,fill opacity=0.300000}]

%% Coordinate of the vertices:
%%
\coordinate (0.86603, -0.50000) at (0.86603, -0.50000);
\coordinate (0.86603, 0.50000) at (0.86603, 0.50000);
\coordinate (0.00000, -1.00000) at (0.00000, -1.00000);
\coordinate (0.00000, 1.00000) at (0.00000, 1.00000);
\coordinate (-0.86603, -0.50000) at (-0.86603, -0.50000);
\coordinate (-0.86603, 0.50000) at (-0.86603, 0.50000);

%% Drawing the interior
%%
\fill[facet] (-0.86603, 0.50000) -- (0.00000, 1.00000) -- (0.86603, 0.50000) -- (0.86603, -0.50000) -- (0.00000, -1.00000) -- (-0.86603, -0.50000) -- cycle {};

%% Drawing edges
%%
\draw[edge] (0.86603, -0.50000) -- (0.86603, 0.50000);
\draw[edge] (0.86603, -0.50000) -- (0.00000, -1.00000);
\draw[edge] (0.86603, 0.50000) -- (0.00000, 1.00000);
\draw[edge] (0.00000, -1.00000) -- (-0.86603, -0.50000);
\draw[edge] (0.00000, 1.00000) -- (-0.86603, 0.50000);
\draw[edge] (-0.86603, -0.50000) -- (-0.86603, 0.50000);

\node[color=norange] at (0,-.5in) {$\O_{(1,1,1)}$};
\end{tikzpicture}