Cellcolor creates too wide coloured field in table without internal cell margins

Question

Summary: can I get a table with narrow columns (about 5 mm), a normally sized capital letter in some cells and some of the cells coloured (filled by a pattern would also work)?

Full question:

I'm trying to create a table with fairly narrow columns (5 mm), in which some cells are gray. Some of the cells (though never any gray cell, if that matters) will contain a single capital letter. In order to keep the column narrow and the letters in default font sice, I'm taking away the column separation by defining each column as @{} m{5mm} @{}. This works well; together with a small \vspace I can get the letters centered vertically and with \centering{} also horizontally.

Problem is, when I try to fill in a single cell using \cellcolor, the colour actually extends to the sides over the cell borders. The command \columncolor has an option for overhang, but as far as I can see, \cellcolor doesn't have this. Is there a way around it?

My code so far:

\documentclass{article}
\usepackage[table]{xcolor} 
\begin{document}

\begin{tabular}{| @{} m{5mm} @{} | @{} m{5mm} @{} | @{} m{5mm} @{} |@{} m{0pt} @{} }
  \hline
  & \vspace{.75mm}\centering{E} & \vspace{.75mm}\centering{C} &\\
  \hline 
  \vspace{0.75mm}
  \centering{P} & \cellcolor{gray!50} & &\\
  \hline 
  \vspace{0.75mm}
  \centering{M} & & &\\
  \hline 
\end{tabular}

\end{document}

Notes on the example:

1) The 0 mm column to the far right is there since the rightmost column, for some reason, cannot contain a \centering. If there's a better solution to this, I'm all ears.

2) The \vspace{0.75mm} is only in order to make the cells square (or very close to square).

Possible workaround: I have thought about instead of using \cellcolor, to insert a grey picture, stretched to the right dimensions, in each cell. This works except for creating a small white gap under the picture, before the \hline. I can move up the line by using \[-1.3 mm], but if I do that on the last line the vertical lines between each column protrudes under the bottom. Either solution would be OK, I have long ago given up the thought of elegant code...

Answer 1

Here is a solution, and some simplification to your code. But do you really need to have a 0pt values for \tabcolsep?

\documentclass{article}
\usepackage[table]{xcolor}

\begin{document}

{\setlength{\tabcolsep}{0pt}%
\begin{tabular}{| >{\centering}m{5mm} | >{\centering} m{5mm} | >{\centering\arraybackslash}m{5mm} |}
  \hline
  & \vspace{.75mm}E & \vspace{.75mm} C \\
  \hline
  \vspace{0.75mm}
   P & \cellcolor{gray!50} & \\
  \hline
  \vspace{0.75mm} M & & \\
  \hline
\end{tabular}}% 

\end{document}

Answer 2

With {NiceTabular} of nicematrix which has its own system for coloring the tabulars, you have directly the expected output.

\documentclass{article}
\usepackage{nicematrix}
\begin{document}

\begin{NiceTabular}{| @{} m{5mm} @{} | @{} m{5mm} @{} | @{} m{5mm} @{} |@{} m{0pt} @{} }[colortbl-like]
  \hline
  & \vspace{.75mm}\centering E & \vspace{.75mm}\centering C &\\
  \hline 
  \vspace{0.75mm}
  \centering P & \cellcolor{gray!50} & &\\
  \hline 
  \vspace{0.75mm}
  \centering M & & &\\
  \hline 
\end{NiceTabular}

\end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).