hexagon placement intuition

Trying to develop some intution for hexagon placement, and perhaps re-discover some trigonometry along the way.

for loops and conditionals?! I know. hopefully more compact representations will present themselves in future iterations.

hexagon path generating function from http://www.thelow.co.uk/?p=128

motivation from the bl.ocks hexbin with no axes and Fog of War III, which stubbornly resisted quick modification

<!DOCTYPE html>
<html>
  <head>
    <meta charset="utf-8">
    <title>hexagon placement intuition</title>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.6/d3.min.js"></script>
    <style>
    </style>
  </head>
  <body>
    <script>
var data = ["A", "B", "C", "D", "E", "F", "G"];

var height = 240;
var width = 460;
var svg = d3.select('body').append('svg')
  .attr("height", height)
  .attr("width", width);

svg.append("clipPath")
    .attr("id", "clip")
  .append("rect")
    .attr("width", width)
    .attr("height", height)

var board = svg.append("g")
  .attr("clip-path", "url(#clip)");

var hexCount = 13;
var r = 20;
var x0 = 100;
var y0 = 100;
var x;
var y;
var xStep = Math.cos(Math.PI/6)*r;
var yStep = Math.sin(Math.PI/6)*r;
var c; // center

for(var i=0; i<hexCount; i++) {

c = hexCenter(i, x0, y0);
  
  var hex = board.append("g")
    .attr("class", "hex");

hex  
    .append("path")
      .attr("d", hexagon(c.x,c.y,r))
      .style("fill", hexColor(i))
      .style("stroke", "black");

hex
    .append("text")
    .style("stroke", "white")
    .style("stroke-width", "1")
    .style("fill", "white")
    .style("opacity", .3)
    .attr({
      "x": c.x,
      "y": c.y,
      "dy": ".35em"
    })
    .style("text-anchor", "middle")
    .text(i); // data[i]
}

function hexagon(x,y,r) {
  var x1 = x;
  var y1 = y-r;
  var x2 = x+(Math.cos(Math.PI/6)*r);
  var y2 = y-(Math.sin(Math.PI/6)*r);
  var x3 = x+(Math.cos(Math.PI/6)*r);
  var y3 = y+(Math.sin(Math.PI/6)*r);
  var x4 = x;
  var y4 = y+r;
  var x5 = x-(Math.cos(Math.PI/6)*r);
  var y5 = y+(Math.sin(Math.PI/6)*r);
  var x6 = x-(Math.cos(Math.PI/6)*r);
  var y6 = y-(Math.sin(Math.PI/6)*r);
  
  var path = "M"+x1+" "+y1+" L"+x2+" "+y2+" L"+x3+" "+y3+" L"+x4+" "+y4+" L"+x5+" "+y5+" L"+x6+" "+y6+"z";
  return path;
}

function hexColor(i) {
  if(i === 0) { return "#006d2c" }
  if(i <   7) { return "#2ca25f" } 
  if(i >=  7) { return "#66c2a4" }
}

</script>
  </body>
</html>

https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.6/d3.min.js