Icosahedron by mbostock

index.html

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

.point {
  fill: #000;
  stroke: #fff;
}

.edge {
  fill: none;
  stroke: #000;
  stroke-opacity: .4;
}

.face {
  fill: #eee;
  fill-rule: nonzero;
}

</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var width = 960,
    height = 500;

var velocity = [.018, .006];

var projection = d3.geo.orthographic()
    .scale(240);

var path = d3.geo.path()
    .projection({
      stream: function(out) {
        return {
          point: function(x, y) { var p = projection([x, y]); out.point(p[0], p[1]); },
          lineStart: function() { out.lineStart(); },
          lineEnd: function() { out.lineEnd(); },
          polygonStart: function() { out.polygonStart(); },
          polygonEnd: function() { out.polygonEnd(); }
        };
      }
    });

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

var face = svg.selectAll(".face")
    .data(icosahedron_faces)
  .enter().append("path")
    .attr("class", "face");

var edge = svg.append("path")
    .datum(icosahedron_edges)
    .attr("class", "edge");

var point = svg.append("path")
    .datum(icosahedron_points)
    .attr("class", "point");

d3.timer(function(elapsed) {
  projection.rotate([elapsed * velocity[0], elapsed * velocity[1]]);
  point.attr("d", path);
  edge.attr("d", path);
  face.attr("d", path);
});

function icosahedron_points() {
  var points = [],
      y = Math.atan2(1, 2) * 180 / Math.PI;
  points.push([0, -90]);
  for (var x = 0; x < 360; x += 36) {
    points.push([x, -y], [x += 36, y]);
  }
  points.push([0, 90]);
  return {type: "MultiPoint", coordinates: points};
}

function icosahedron_edges() {
  var edges = [],
      y = Math.atan2(1, 2) * 180 / Math.PI;
  for (var x = 0; x < 360; x += 72) {
    edges.push([[x +  0, -90], [x +  0,  -y]]);
    edges.push([[x +  0,  -y], [x + 72,  -y]]);
    edges.push([[x + 36,   y], [x - 36,   y]]);
    edges.push([[x + 36,   y], [x +  0,  -y]]);
    edges.push([[x - 36,   y], [x +  0,  -y]]);
    edges.push([[x + 36,  90], [x + 36,   y]]);
  }
  return {type: "MultiLineString", coordinates: edges};
}

function icosahedron_faces() {
  var faces = [],
      y = Math.atan2(1, 2) * 180 / Math.PI;
  for (var x = 0; x < 360; x += 72) {
    faces.push([[[x +  0, -90], [x +  0,  -y], [x + 72,  -y], [x +  0, -90]]]);
    faces.push([[[x +  0,  -y], [x + 72,  -y], [x + 36,   y], [x +  0,  -y]]]);
    faces.push([[[x + 36,   y], [x +  0,  -y], [x - 36,   y], [x + 36,   y]]]);
    faces.push([[[x - 36,  90], [x - 36,   y], [x + 36,   y], [x + 36,  90]]]);
  }
  return faces.map(function(face) {
    return {type: "Polygon", coordinates: face};
  });
}

</script>