Peirce Quincuncial Projection

The Peirce quincuncial projection can be constructed using d3.geo.guyou from the geo.projection D3 plugin.

<!DOCTYPE html>
<meta charset="utf-8">
<style>

body {
  padding: 51px 281px;
}

.background {
  fill: #a4bac7;
}

.foreground {
  fill: none;
  stroke: #333;
  stroke-width: 1.5px;
}

.graticule {
  fill: none;
  stroke: #fff;
  stroke-width: .5px;
}

.graticule:nth-child(2n) {
  stroke-dasharray: 2,2;
}

.land {
  fill: #d7c7ad;
  stroke: #766951;
}

.boundary {
  fill: none;
  stroke: #a5967e;
}

</style>
<body>
<script src="https://d3js.org/d3.v3.min.js"></script>
<script src="https://cdn.jsdelivr.net/gh/d3/d3-plugins/geo/projection/projection.js"></script>
<script>

var width = 397,
    height = 397,
    π = Math.PI;

var front = [90, 0],
    back = [270, 0];

function sgn(x) {
  return x > 0 ? 1 : x < 0 ? -1 : 0;
}

var guyou = d3.geo.guyou().translate([0, 0]).scale(1);

var projection = d3.geo.projection(function(λ, φ) {
      var t = Math.abs(λ) < π / 2,
          coordinates = guyou([(t ? λ : -sgn(λ) * (π - Math.abs(λ))) * 180 / π, φ * 180 / π]),
          x = coordinates[0] / Math.SQRT2 - coordinates[1] / Math.SQRT2,
          y = coordinates[1] / Math.SQRT2 + coordinates[0] / Math.SQRT2;
      if (t) return [x, y];
      var d = 2 * 1.311028777082283, // TODO unobfuscate
          s = (x > 0) ^ (y > 0) ? -1 : 1;
      return [s * x - sgn(y) * d, s * y - sgn(x) * d];
    })
    .scale(75)
    .rotate([0, -90, 45])
    .translate([width / 2 - .5, height / 2 - .5])
    .clipAngle(180 - 1e-6);

var path = d3.geo.path()
    .projection(projection);

var center = projection([0, 90]),
    w = Math.abs(projection([90, 0])[0] - projection([-90, 0])[0]);

center[0] -= w / 2;
center[1] -= w / 2;

var graticule = d3.geo.graticule()
    .step([15, 15]);

var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height)
  .append("g")
    .attr("transform", "translate(1.5,1.5)");

svg.append("rect")
    .attr("class", "background")
    .attr("x", center[0])
    .attr("y", center[1])
    .attr("width", w)
    .attr("height", w);

svg.selectAll(".graticule")
    .data(graticule.lines)
  .enter().append("path")
    .attr("class", "graticule")
    .attr("d", path);

svg.append("rect")
    .attr("class", "foreground")
    .attr("x", center[0])
    .attr("y", center[1])
    .attr("width", w)
    .attr("height", w);

d3.json("readme-boundaries.json", function(err, collection) {
  svg.insert("g", ".graticule")
      .attr("class", "boundary")
    .selectAll("path")
      .data(collection.geometries)
    .enter().append("path")
      .attr("d", path);
});

d3.json("readme-land.json", function(err, collection) {
  svg.insert("g", ".graticule,.boundary")
      .attr("class", "land")
    .selectAll("path")
      .data(collection.geometries)
    .enter().append("path")
      .attr("d", path);
});

</script>

Modified http://d3js.org/d3.v3.min.js to a secure url

Updated missing url https://raw.github.com/d3/d3-plugins/master/geo/projection/projection.js to https://cdn.jsdelivr.net/gh/d3/d3-plugins/geo/projection/projection.js

https://d3js.org/d3.v3.min.js

https://raw.github.com/d3/d3-plugins/master/geo/projection/projection.js