Strange Arrow length

Question

I wish my arrows have the same size. For example, I can not explain why the two vertical arrows coming out of the vertex "a" have different sizes.

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{amsmath}
\begin{document}
$$
\begin{tikzcd} [column sep=small , row sep=small ] 
&&& \bullet \ar{dl} \ar{dr}&&& \\
&& \bullet \ar{dl}& \vdots \ar{u}& \bullet \ar{dr}&& \\
& \iddots \ar{dl}&& \bullet \ar{u}&& \ddots \ar{dr}& \\
\bullet \ar{r}& \dotsc \ar{r}& \bullet \ar{r}& a \ar{u} \ar{d}& \bullet \ar{l}& \dotsc \ar{l}& \bullet \ar{l}\\
& \ddots \ar{ul}&& \bullet \ar{d}&& \iddots \ar{ur}& \\
&& \bullet  \ar{ul}& \vdots \ar{d}& \bullet \ar{ur}&& \\
&&& \bullet \ar{ul} \ar{ur}&&& 
\end{tikzcd}
$$
\end{document}

Answer 1

You will need to set the column and row distance in respect to the cells centre. I adapted some of the dots for you. I stretched the whole thing a bit in order to get the same angle as for the \ddots. If you want a symmetrical diagram, you will have to rotate those dots a bit.

% arara: pdflatex

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{mathtools}
\usepackage{mathdots}
\makeatletter
\DeclareRobustCommand{\rvdots}{%
    \vbox{
        \baselineskip4\p@\lineskiplimit\z@
        \kern-\p@
        \hbox{.}\hbox{.}\hbox{.}
    }}
    \makeatother

\begin{document}
\[
    \begin{tikzcd} [column sep={1.32cm,between origins} , row sep={1cm,between origins} ] 
    &&& \bullet \ar{dl} \ar{dr}&&& \\
    && \bullet \ar{dl}& \rvdots \ar{u}& \bullet \ar{dr}&& \\
    & \iddots \ar{dl}&& \bullet \ar{u}&& \ddots \ar{dr}& \\
    \bullet \ar{r}& \cdots \ar{r}& \bullet \ar{r}& a \ar{u} \ar{d}& \bullet \ar{l}& \cdots \ar{l}& \bullet \ar{l}\\
    & \ddots \ar{ul}&& \bullet \ar{d}&& \iddots \ar{ur}& \\
    && \bullet  \ar{ul}& \rvdots \ar{d}& \bullet \ar{ur}&& \\
    &&& \bullet \ar{ul} \ar{ur}&&& 
    \end{tikzcd}
\]
\end{document}

---

You may need less tweaking if you use the following approach:

% arara: pdflatex

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

\begin{document}
\[
    \begin{tikzcd} [column sep={1cm,between origins} , row sep={1cm,between origins} ] 
        & & & \bullet \ar{dl} \ar{dr} & & & \\
        & & \bullet \ar{ddll}[description,sloped]{\dots} & & \bullet \ar{ddrr}[description,sloped]{\dots} & & \\
        & & & \bullet \ar{uu}[description,sloped]{\dots} & & & \\
        \bullet \ar{rr}[description]{\dots} & & \bullet \ar{r} & a \ar{u} \ar{d}& \bullet \ar{l} & & \bullet \ar{ll}[description]{\dots}\\
        & \ar{ul}&& \bullet \ar{dd}[description,sloped]{\dots} & & & \\
        & & \bullet  \ar{uull}[description,sloped]{\dots} & & \bullet \ar{uurr}[description,sloped]{\dots} & & \\
        & & & \bullet \ar{ul} \ar{ur} & & & 
    \end{tikzcd}
\]
\end{document}