Program written

I've finally written the program for this chunk, it justs needs commenting and then the chunk text explanation writing:

void setup() {

  size(800, 600, P3D);

}

void draw() {

  float clockwiseDirection = frameCount * PI;
  float antiClockwiseDirection = frameCount * -PI;

  background(255);
  fill(138, 43, 226, 100);

  pushMatrix();
  // move to the centre of the screen
  translate(width / 2, height / 2, 0);

  rotateX(clockwiseDirection / 250);
  rotateY(clockwiseDirection / 250);
  rotateZ(clockwiseDirection / 250);
  cuboctahedron(250);

  rotateX(antiClockwiseDirection / 250);
  rotateY(antiClockwiseDirection / 250);
  rotateZ(antiClockwiseDirection / 250);
  sphereDetail(1);
  sphere(200);

  rotateX(clockwiseDirection / 200);
  rotateY(clockwiseDirection / 200);
  rotateZ(clockwiseDirection / 200);
  box(120);

  rotateX(antiClockwiseDirection / 150);
  rotateY(antiClockwiseDirection / 150);
  rotateZ(antiClockwiseDirection / 150);
  cuboctahedron(50);

  popMatrix();

  for (int i = 40; i < height + 40; i = i + 80) {
    for (int j = 40; j < width; j = j + 80) {

      pushMatrix();
      translate(j, i, 0);

      rotateZ(antiClockwiseDirection / 150);
      rotateX(antiClockwiseDirection / 150);
      rotateY(antiClockwiseDirection / 150);
      draw2DPolygon(6, 40);

      rotateZ(clockwiseDirection / 255);
      rotateX(clockwiseDirection / 255);
      rotateY(clockwiseDirection / 255);
      draw2DPolygon(5, 30);

      popMatrix();

    }
  }

}

void draw2DPolygon(int sides, int size) {

  fill(85, 26, 139, 30);
  stroke(138, 43, 226, 20);

  int x = 0;
  int y = 0;

  float centreX = 0;
  float centreY = 0;

  for (int i = 0; i < sides; i++) {

    float xCoord = (x + size * cos(i * 2 * PI / sides));
    float yCoord = (y + size * sin(i * 2 * PI / sides));

    centreX += xCoord;
    centreY += yCoord;

  }

  centreX = (centreX / sides) * -1;
  centreY = (centreY / sides) * -1;

  beginShape();

  for (int i = 0; i <= sides; i++) {

    float xCoord = (centreX + size * cos(i * 2 * PI / sides));
    float yCoord = (centreY + size * sin(i * 2 * PI / sides));

    vertex(xCoord, yCoord);

  }

  endShape();

  for (int i = 0; i < sides; i++) {

    float xCoord = (centreX + size * cos(i * 2 * PI / sides));
    float yCoord = (centreY + size * sin(i * 2 * PI / sides));

    line(xCoord, yCoord, centreX, centreY);

  }

  stroke(0);

}

void cuboctahedron(int size) {

  char[] vertices = new char[] {
    'A',
    'I',
    'E',
    'K',
    'A',
    'B',
    'J',
    'F',
    'I',
    'B',
    'D',
    'L',
    'H',
    'J',
    'D',
    'C',
    'K',
    'G',
    'L',
    'C',
    'A',
    'I',
    'E',
    'G',
    'H',
    'F',
    'E'  };

  beginShape();
  drawCuboctahedron(vertices, size);
  endShape();

}

void drawCuboctahedron(char[] vertices, float edgeSize) {

  float halfEdgeSize = edgeSize / 2;
  float halfDiagonalSize = (sqrt((sq(edgeSize)) + (sq(edgeSize)))) / 2;

  float x = 0;
  float y = 0;
  float z = -edgeSize;

  for (int i = 0; i < vertices.length; i++) {
    char vertex = vertices[i];
    switch (vertex) {
    case 'A':
      vertex(x - halfEdgeSize, y - halfDiagonalSize, z + halfEdgeSize);
      break;
    case 'B':
      vertex(x + halfEdgeSize, y - halfDiagonalSize, z + halfEdgeSize);
      break;
    case 'C':
      vertex(x - halfEdgeSize, y - halfDiagonalSize, z + (halfEdgeSize * 3));
      break;
    case 'D':
      vertex(x + halfEdgeSize, y - halfEdgeSize, z + (halfEdgeSize * 3));
      break;
    case 'E':
      vertex(x - halfEdgeSize, y + halfEdgeSize, z + halfEdgeSize);
      break;
    case 'F':
      vertex(x + halfEdgeSize, y + halfEdgeSize, z + halfEdgeSize);
      break;
    case 'G':
      vertex(x - halfEdgeSize, y + halfDiagonalSize, z + (halfEdgeSize * 3));
      break;
    case 'H':
      vertex(x + halfEdgeSize, y + halfDiagonalSize, z + (halfEdgeSize * 3));
      break;
    case 'I':
      vertex(x, y, z);
      break;
    case 'J':
      vertex(x + (halfEdgeSize * 2), y, z + (halfEdgeSize * 2));
      break;
    case 'K':
      vertex(x - (halfEdgeSize * 2), y, z + (halfEdgeSize * 2));
      break;
    case 'L':
      vertex(x, y, z + (halfEdgeSize * 4));
      break;
    }
  }

}