How to produce this rectangle of hexagonal grids with triangles and squares in tikz?

Question

I would like to produce this picture with tikz.

I start with this code and its output:

CODE:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{shapes.geometric,arrows.meta,calc,decorations.markings,math,arrows.meta}
\usetikzlibrary{plotmarks}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[x=7.5mm,y=4.34mm]
  %   some styles
  \tikzset{
  box/.style={
  regular polygon,
  regular polygon sides=6,
  minimum size=10mm,
  inner sep=0mm,
  outer sep=0mm,
  rotate=0,
  draw
}
}
\foreach \i in {0,...,5} 
  \foreach \j in {0,...,5} {
  \node[box] at (2\i,2\j) {};
  \node[box] at (2\i+1,2\j+1) {};
}
  \draw[->] (-1,0) -- (13,0) node[anchor = north west] {$x$};
  \draw[->] (0,-1.5) -- (0,13) node[anchor = south east] {$y$};
    \node[draw=black,fill=black,rectangle,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt] at (4,4) {};
   \node[draw=black,fill=black,rectangle,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt] at (8,8) {};
   \node[draw=red,fill=red,isosceles triangle,isosceles triangle stretches,shape border rotate=90,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt] at (3,0) {};
   \node[draw=red,fill=red,isosceles triangle,isosceles triangle stretches,shape border rotate=90,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt] at (3,3) {};
   \node[draw=red,fill=red,isosceles triangle,isosceles triangle stretches,shape border rotate=90,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt] at (5,2) {};
\end{tikzpicture}
\end{document}

OUTPUT:

1. I cannot produce the coordinates in the x-axis and y-axis (the numbers);
2. I cannot positions the black squares and the red triangles at the vertices of the hexagons as shown; and
3. I cannot remove the hexagons that exceeds the x-axis and the y-axis.

Thank you for your help.

NB. The code of the hexagonal grids I found it somewhere in this site but I cannot remember the link for it. The triangles and the squares are taken from this link https://tex.stackexchange.com/a/188535/80848

Answer 1

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}
\tikzset
  {tri/.style = % red triangles (needs shapes.geometric)
    {draw=red,fill=red,isosceles triangle,isosceles triangle stretches,
     shape border rotate=90,minimum width=0.2cm,minimum height=0.2cm,
     inner sep=0pt
    },
   box/.style = % black squares
    {draw=black,fill=black,rectangle,minimum width=0.2cm,
     minimum height=0.2cm,inner sep=0pt
    }
  }
\begin{tikzpicture}[x=0.1mm,y=0.1mm]
  \newcommand\side{57.735} % hex side = hex height / (2*sin(60)) = hex height / sqrt(3)
  \begin{scope}[draw=blue] % scope for hexagon grid
    \clip (0,0) rectangle (1000,501); % clipping confines grid to rectangle
    \foreach \i in {0,...,6} % seven towers of hexagons
      \foreach \j in {0,...,5} % each six hexagons high
        {\begin{scope}[shift={({\i*3*\side},{\j*100})}] % scope for one hexagon
          \foreach \k in {0,60,...,300}
            \draw (\k:\side) -- ({\k+60}:\side); % draw hexagon using polar coordinates
          \draw (\side,0) -- ({2*\side},0); % draw a horizontal extender connecting neighbouring hexagon towers
         \end{scope}
        }
  \end{scope}
  % x axis
  \draw (0,0) -- (1000,0);
  \foreach \i in {0,100,...,1000} do
    \draw (\i,0) node[below]{\tiny \i} -- (\i,10);
  % y axis
  \draw (0,0) -- (0,500);
  \foreach \i in {0,100,...,500} do
    \draw (0,\i) node[left]{\tiny \i} -- (10,\i);
  % marks
  \node[tri] at ({2*\side},300) {};
  \node[tri] at ({2.5*\side},450) {};
  \node[box] at ({3.5*\side},250) {};
  \node[tri] at ({4*\side},100) {};
  \node[tri] at ({5.5*\side},150) {};
  \node[tri] at ({5.5*\side},250) {};
  \node[tri] at ({8.5*\side},50) {};
  \node[tri] at ({10*\side},400) {};
  \node[tri] at ({11.5*\side},450) {};
  \node[tri] at ({11.5*\side},350) {};
  \node[box] at ({12.5*\side},250) {};
  \node[tri] at ({17*\side},100) {};
\end{tikzpicture}
\end{document}

Answer 2

Number 3 can be obtained using a scope environment together with \clip to remove the polygon parts outside the axis. I guess both problems 1 and 2 comes from the scaling. First of all the x and y axis are in the order of 100s, meaning if we want to draw using that scale we need to set e.g. x=0.1mm,y=0.1mm. A hexagon with height 100 between the upper and lower side then has the width 115.47 (i.e. 2*5/cos pi/6), and each side half the width. Since the polygon should be given in real measures the scaling gives the size of it as 11.547mm (the width, height and size of the polygon are given in terms of the size of a circle defined by its corners). Then it is just to start counting squares:-)

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
%\usepackage{pgfplots}
\usetikzlibrary{shapes.geometric,arrows.meta,calc,decorations.markings,math,arrows.meta}
%\usetikzlibrary{plotmarks}
%\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[%
  x=0.1mm,y=0.1mm,
  box/.style={
    gray!60,
    regular polygon,
    regular polygon sides=6,
    minimum size=11.547mm,
    inner sep=0mm,
    outer sep=0mm,
    rotate=0,
    draw},
  blsq/.style={draw=black,fill=black,rectangle,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt},
  redtr/.style={draw=red,fill=red,isosceles triangle,isosceles triangle stretches,shape border rotate=90,minimum width=0.2cm,minimum height=0.2cm,inner sep=0pt}
  ]

  \pgfmathsetmacro\PolyWidth{115.47}
  %%% Grid
  \begin{scope}
    \clip (0,0) rectangle (1050,501);
    \foreach \x in {0,1,...,5}{
      \foreach \y in {0,1,...,4}{
        \node[box] at (\x*1.5*\PolyWidth,\y*100){};
        \node[box] at (\x*1.5*\PolyWidth+0.75*\PolyWidth,\y*100+50){};
      }
    }
  \end{scope}
  %%% Marks
  \foreach \x/\y/\type in{%
    1/3/redtr,
    1.25/4.5/redtr,
    1.75/2.5/blsq,
    2/1/redtr,
    2.75/1.5/redtr,
    2.75/2.5/redtr,
    4.25/0.5/redtr,
    5/4/redtr,
    5.75/3.5/redtr,
    5.75/4.5/redtr,
    6.25/2.5/blsq,
    8.5/1/redtr}
  \node[\type] at (\x*\PolyWidth,\y*100){};
  %%% Axis
  \draw[->] (-10,0) -- (1100,0) node[anchor = north west] {$x$};
  \foreach \x in {0,100,...,1000}{%% X-tick marks
    \draw (\x,0) node[below]{\x}--+(0,10);
  }  
  \draw[->] (0,-10) -- (0,550) node[anchor = south east] {$y$};
  \foreach \y in {0,50,...,500}{%% Y-tick marks
    \draw (0,\y) node[left]{\y}--+(10,0);
  }
\end{tikzpicture}
\end{document}