drawing type of commutative diagram

I drawn a commutative diagram with this code

    \documentclass{article}
\usepackage{tikz-cd}
\usepackage{etoolbox}

\begin{document}
$$\begin{tikzcd}[arrows] \node(P0) at (90:2.6cm){V}; \node(P1) at (90+72:2.5cm){X} ; \node(P2) at (90+2*72:4cm){Y}; \node(P3) at (90+3*72:4cm){W}; \node(P4) at (90+4*72:2.5cm){U}; \node(P5) at (270+5*72:4.6cm){Z}; \arrow[from=P1,to=P0,"f_{1}"'] \arrow[from=P0,to=P4,"f_{2}"'] \arrow[from=P1,to=P4,"f_{3}"'] \arrow[from=P1,to=P3,"f_{4}"] \arrow[from=P1,to=P2,"f_{6}"] \arrow[from=P4,to=P3,"f_{5}"] \arrow[from=P2,to=P5,"f_{7}"] \arrow[from=P5,to=P3,"f_{8}"] \end{tikzcd}$$
\end{document}


but this picture is very big and I want sth smaller than this, such that Y and W be nearer to X and U. How could I fix it?

The trick is to add some vertical space between rows 2 and 3. Almost no explicit lengths are needed.

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}

$\begin{tikzcd} & V \arrow[dr,"f_2"] \\ X \arrow[ur,"f_1"] \arrow[rr,"f_3"] \arrow[drr,"f_4"] \arrow[d,"f_6"'] && U \arrow[d,"f_5"] \\[2em] Y \arrow[dr,"f_7"'] && W \\ & Z \arrow[ur,"f_8"'] \end{tikzcd}$

\end{document}


I changed some label positions, fix them to your liking. Experiment with the 2em and shorten it a bit to get a more "hexagon-like” shape.

I like very much...how alternative to the classic tikz-cd also xy package. I add my MWE with the distance of the rows @R of 2.5pc. Peraphs it could be similar to an hexagon :-) like the code of @egreg :-); you can adjiust the hexagon with rows and columns changing the parameters of the dots \xymatrix@R=...pc@C=....pc.

\documentclass[a4paper,12pt]{article}
\usepackage[all,cmtip]{xy}

\begin{document}

\xymatrix@R=2.5pc{
& V \ar[dr]^{f_2}& \\
X \ar[rr]^{f_3} \ar[ur]^{f_1} \ar[d]_{f_6} \ar[drr]^{f_4} &  & U\ar[d]^{f_5} \\
Y \ar[dr]_{f_7}&  & W\\
& Z \ar[ur]_{f_8}&
}
\end{document}


PS: You have the straight lines zooming in....It is an optical effect of the output.