geoGringortenQuincuncial inverse, fixed by fil

index.html

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

.stroke {
  fill: none;
  stroke: #000;
  stroke-width: 3px;
}

.fill {
  fill: #fff;
}

.graticule {
  fill: none;
  stroke: #777;
  stroke-width: 0.5px;
  stroke-opacity: 0.5;
}

.land {
  fill: #222;
}

.boundary {
  fill: none;
  stroke: #fff;
  stroke-width: 0.5px;
}

</style>
<svg width="960" height="500"></svg>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="d3-geo-projection.js"></script>
<script src="https://d3js.org/topojson.v1.min.js"></script>
<script>

var svg = d3.select("svg"),
    width = +svg.attr("width"),
    height = +svg.attr("height");

var projection = d3.geoGringortenQuincuncial().scale(160);

var graticule = d3.geoGraticule();

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

var defs = svg.append("defs");

defs.append("path")
    .datum({type: "Sphere"})
    .attr("id", "sphere")
    .attr("d", path);

defs.append("clipPath")
    .attr("id", "clip")
  .append("use")
    .attr("xlink:href", "#sphere");

svg.append("use")
    .attr("class", "stroke")
    .attr("xlink:href", "#sphere");

svg.append("use")
    .attr("class", "fill")
    .attr("xlink:href", "#sphere");

svg.append("path")
    .datum(graticule)
    .attr("class", "graticule")
    .attr("clip-path", "url(#clip)")
    .attr("d", path);

  
d3.range(-179, 179, 8)
.forEach(lon => d3.range(-89, 89, 8)
  .forEach(lat => {
    var o = [lon, lat],
        m = projection(o),
        i = projection.invert(m);

    svg.append("path")
  .attr("fill", Math.abs(o[0]-i[0]) + Math.abs(o[1]-i[1]) < 0.1 ? "green" : "red")
    .attr("d", path({type:"Point", coordinates: o}))
  }))
var marker = svg.append("path")
  .attr("fill", "orange")

svg.on('mousemove', function() {
  var mouse = d3.mouse(this);
  marker.attr("d", path({type:"Point", coordinates: projection.invert(mouse)}));
});


d3.json("https://gist.githubusercontent.com/mbostock/4090846/raw/d534aba169207548a8a3d670c9c2cc719ff05c47/world-50m.json", function(error, world) {
  if (error) throw error;

  svg.insert("path", ".graticule")
      .datum(topojson.feature(world, world.objects.land))
      .attr("class", "land")
      .attr("clip-path", "url(#clip)")
      .attr("d", path);

  svg.insert("path", ".graticule")
      .datum(topojson.mesh(world, world.objects.countries, function(a, b) { return a !== b; }))
      .attr("class", "boundary")
      .attr("clip-path", "url(#clip)")
      .attr("d", path);
});

</script>