Here's a sketch, produced with a vector-based drawing app, of the figure that I wish to produce in TikZ:
Here's an initial draft of TikZ, which only shows a 4-sided cone:
\documentclass[tikz]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{100}
\begin{tikzpicture}[tdplot_main_coords]
\coordinate (O) at (0,0,0);
\coordinate (e1) at (1,0,1);
\coordinate (e2) at (0,1,1);
\coordinate (e3) at (-1,0,1);
\coordinate (e4) at (0,-1,1);
% Level sets
\foreach \scale in {1.0,.75,.50,.25}
\draw[scale=\scale,fill opacity=.5,fill=gray]
(1,0,0) -- (0,1,0) -- (-1,0,0) -- (0,-1,0) -- cycle;
% Cone
\draw (e1) -- (e2) -- (e3) -- (e4) -- cycle;
% Extreme rays
\draw[line join=round,fill,opacity=.7] (O) -- (e1) -- (e2) -- cycle;
\draw[line join=round,fill,opacity=.7] (O) -- (e1) -- (e4) -- cycle;
\draw[line join=round,fill,opacity=.5] (O) -- (e4) -- (e3) -- cycle;
\draw[line join=round,fill,opacity=.5] (O) -- (e3) -- (e2) -- cycle;
\end{tikzpicture}
\end{document}
Is tikz-3dplot
the best way to go about this? I'll be glad for pointers on getting the right look.
Update
Thanks to marmot's answer, I was able to produce this illustration:
And here's marmot's modified code:
\documentclass[10pt,tikz,multi]{standalone}
\usepackage{amsmath,amssymb}
\usepackage{tikz-3dplot}
\usetikzlibrary{shapes.geometric}
\begin{document}
\tdplotsetmaincoords{68}{95}
\begin{tikzpicture}[very thin,tdplot_main_coords,line join=round]
% Draw top of cone
\begin{scope}[canvas is xy plane at z=6,transform shape]
\node[regular polygon,regular polygon sides=5,minimum width=6cm](5gon){};
\end{scope}
% Level sets
\begin{scope}[canvas is xy plane at z=0,transform shape]
\draw (-3,-2.6) rectangle (4,2.6);
\foreach \X in {5,4,...,1} {
\node[draw=black,regular polygon,regular polygon sides=5,
minimum width=\X cm,fill=gray,fill opacity=0.2](5gon-\X){};
}
\node[thick,draw=blue,regular polygon,regular polygon sides=5,draw,minimum
width=5cm,fill=gray,fill opacity=0.2](5gon-5){};
% Labels
\node at (-2.5,2.1) [rotate=90,scale=2] {$\mathbb{R}$};
\node at (+2.6,-.75) [rotate=90,scale=2] {$\mathcal{C}$};
\end{scope}
% Faces of cone
\foreach \X [count=\Y] in {2,3,4,5,1}
{\draw \ifnum\Y<4
[fill=orange]
\else
[fill=gray,opacity=.9]
\fi (5gon.corner \Y) -- (0,0,0) -- (5gon.corner \X) -- cycle;}
% Slice cone at unit level
\begin{scope}[canvas is xy plane at z=5,transform shape]
\node[draw=blue,thick,fill=gray,opacity=.4,
regular polygon,regular polygon sides=5,minimum width=5cm]{};
\node at (-.5,-.1) [rotate=90,scale=1.2] {$\mathcal{C}\times\{1\}$};
\end{scope}
\end{tikzpicture}
\end{document}
The lines in the background probably should be dotted, but this version seems fairly complete.