Drawing an arc between two 3D points - tikz

Question

I am trying to draw composite 3D shapes, and I am struggling drawing arcs between two 3D points. In the example below I would like to draw a dashed arc of 180 degrees between from D to H clockwise, and a solid arc of 180 degrees from D to H anti-clockwise. However, when I try
\draw (D) arc[radius=\R, start angle=180, end angle=0];
I don't get the arc I want. Below is the code I have so far:
\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{65}{-43}
\begin{center}
\begin{tikzpicture}[
scale=1,
tdplot_main_coords]
\def\R{2}
\def\h{6}
\coordinate (A) at ({\R*cos(0)},{\R*sin(0)},0);
\coordinate (B) at ({\R*cos(45)},{\R*sin(45)},0);
\coordinate (C) at ({\R*cos(90)},{\R*sin(90)},0);
\coordinate (D) at ({\R*cos(135)},{\R*sin(135)},0);
\coordinate (E) at ({\R*cos(180)},{\R*sin(180)},0);
\coordinate (F) at ({\R*cos(225)},{\R*sin(225)},0);
\coordinate (G) at ({\R*cos(270)},{\R*sin(270)},0);
\coordinate (H) at ({\R*cos(315)},{\R*sin(315)},0);
\coordinate (O) at (0,0,0);
\coordinate (O') at (0,0,\h);
\coordinate (O'') at (0,0,-\h);
\foreach \i in {A,B,C}{
\draw[dashed] (\i) -- (O');
\node at (\i) [above]{$\i$};}
\foreach \i in {D,E,F,G,H}{
\draw (\i) -- (O');
\node at (\i) [below]{$\i$};}
\draw[red] (O) circle (\R);
\draw[red] (D) -- (O'') -- (H);
\draw[dashed] (H) -- (A) -- (B) -- (C) -- (D);
\draw (D) -- (E) -- (F) -- (G) -- (H);
\node at (O') [above]{$O'$};
\node at (O'') [below,thick,red]{$O''$};
\end{tikzpicture}
\end{center}
\end{document}

Answer 1

Since nobody answered or commented, I came up with my own solution, which is using a two-coordinate system instead of three, but it works...
\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\begin{center}
\begin{tikzpicture}[scale=1]
\def\xRadius{2}
\def\yRadius{0.4*\xRadius}
\def\h{5.4}
\coordinate (A) at ({\xRadius*cos(45)},{\yRadius*sin(45)});
\coordinate (B) at ({\xRadius*cos(90)},{\yRadius*sin(90)});
\coordinate (C) at ({\xRadius*cos(135)},{\yRadius*sin(135)});
\coordinate (D) at ({\xRadius*cos(180)},{\yRadius*sin(180)});
\coordinate (E) at ({\xRadius*cos(225)},{\yRadius*sin(225)});
\coordinate (F) at ({\xRadius*cos(270)},{\yRadius*sin(270)});
\coordinate (G) at ({\xRadius*cos(315)},{\yRadius*sin(315)});
\coordinate (H) at ({\xRadius*cos(0)},{\yRadius*sin(0)});
\coordinate (O) at (0,0);
\coordinate (O') at (0,\h);
\coordinate (O'') at (0,-\h);
\foreach \i in {A,B,C}{
\draw[dashed] (\i) -- (O');
\node at (\i) [above]{$\i$};}
\foreach \i in {D,E,F,G,H}{
\draw (\i) -- (O');
\node at (\i) [below]{$\i$};}
\draw[red,dashed] (H) arc [x radius = \xRadius, y radius = \yRadius, start angle=0, end angle=180];
\draw[red] (H) arc [x radius = \xRadius, y radius = \yRadius, start angle=0, end angle=-180];
\draw[red] (D) -- (O'') -- (H);
\draw[dashed] (H) -- (A) -- (B) -- (C) -- (D);
\draw (D) -- (E) -- (F) -- (G) -- (H);
\node at (O') [above]{$O'$};
\node at (O'') [below,thick,red]{$O''$};
\end{tikzpicture}
\end{center}
\end{document}