class Icosahedron extends Shape3D{

  // icosahedron
  Vector3D topPoint;
  Vector3D[] topPent = new Vector3D[5];
  Vector3D bottomPoint;
  Vector3D[] bottomPent = new Vector3D[5];
  float angle = 0, radius = 150;
  float triDist;
  float triHt;
  float a, b, c;

  // constructor
  Icosahedron(float radius){
    this.radius = radius;
    init();
  }

  Icosahedron(Vector3D v, float radius){
    super(v);
    this.radius = radius;
    init();
  }

  // calculate geometry
  void init(){
    c = dist(cos(0)*radius, sin(0)*radius, cos(radians(72))*radius,  sin(radians(72))*radius);
    b = radius;
    a = (float)(Math.sqrt(((c*c)-(b*b))));

    triHt = (float)(Math.sqrt((c*c)-((c/2)*(c/2))));

    for (int i=0; i<topPent.length; i++){
      topPent[i] = new Vector3D(cos(angle)*radius, sin(angle)*radius, triHt/2.0f);
      angle+=radians(72);
    }
    topPoint = new Vector3D(0, 0, triHt/2.0f+a);
    angle = 72.0f/2.0f;
    for (int i=0; i<topPent.length; i++){
      bottomPent[i] = new Vector3D(cos(angle)*radius, sin(angle)*radius, -triHt/2.0f);
      angle+=radians(72);
    }
    bottomPoint = new Vector3D(0, 0, -(triHt/2.0f+a));
  }

  // draws icosahedron 
  void create(){
    for (int i=0; i<topPent.length; i++){
      // icosahedron top
      beginShape();
      if (i<topPent.length-1){
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+topPoint.x, y+topPoint.y, z+topPoint.z);
        vertex(x+topPent[i+1].x, y+topPent[i+1].y, z+topPent[i+1].z);
      } 
      else {
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+topPoint.x, y+topPoint.y, z+topPoint.z);
        vertex(x+topPent[0].x, y+topPent[0].y, z+topPent[0].z);
      }
      endShape(CLOSE);

      // icosahedron bottom
      beginShape();
      if (i<bottomPent.length-1){
        vertex(x+bottomPent[i].x, y+bottomPent[i].y, z+bottomPent[i].z);
        vertex(x+bottomPoint.x, y+bottomPoint.y, z+bottomPoint.z);
        vertex(x+bottomPent[i+1].x, y+bottomPent[i+1].y, z+bottomPent[i+1].z);
      } 
      else {
        vertex(x+bottomPent[i].x, y+bottomPent[i].y, z+bottomPent[i].z);
        vertex(x+bottomPoint.x, y+bottomPoint.y, z+bottomPoint.z);
        vertex(x+bottomPent[0].x, y+bottomPent[0].y, z+bottomPent[0].z);
      }
      endShape(CLOSE);
    }

    // icosahedron body
    for (int i=0; i<topPent.length; i++){
      if (i<topPent.length-2){
        beginShape();
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+bottomPent[i+1].x, y+bottomPent[i+1].y, z+bottomPent[i+1].z);
        vertex(x+bottomPent[i+2].x, y+bottomPent[i+2].y, z+bottomPent[i+2].z);
        endShape(CLOSE);

        beginShape();
        vertex(x+bottomPent[i+2].x, y+bottomPent[i+2].y, z+bottomPent[i+2].z);
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+topPent[i+1].x, y+topPent[i+1].y, z+topPent[i+1].z);
        endShape(CLOSE);
      } 
      else if (i==topPent.length-2){
        beginShape();
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+bottomPent[i+1].x, y+bottomPent[i+1].y, z+bottomPent[i+1].z);
        vertex(x+bottomPent[0].x, y+bottomPent[0].y, z+bottomPent[0].z);
        endShape(CLOSE);

        beginShape();
        vertex(x+bottomPent[0].x, y+bottomPent[0].y, z+bottomPent[0].z);
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+topPent[i+1].x, y+topPent[i+1].y, z+topPent[i+1].z);
        endShape(CLOSE);
      }
      else if (i==topPent.length-1){
        beginShape();
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+bottomPent[0].x, y+bottomPent[0].y, z+bottomPent[0].z);
        vertex(x+bottomPent[1].x, y+bottomPent[1].y, z+bottomPent[1].z);
        endShape(CLOSE);

        beginShape();
        vertex(x+bottomPent[1].x, y+bottomPent[1].y, z+bottomPent[1].z);
        vertex(x+topPent[i].x, y+topPent[i].y, z+topPent[i].z);
        vertex(x+topPent[0].x, y+topPent[0].y, z+topPent[0].z);
        endShape(CLOSE);
      }
    }
  }

  // overrided methods fom Shape3D
  void rotZ(float theta){
    float tx=0, ty=0, tz=0;
    // top point
    tx = cos(theta)*topPoint.x+sin(theta)*topPoint.y;
    ty = sin(theta)*topPoint.x-cos(theta)*topPoint.y;
    topPoint.x = tx;
    topPoint.y = ty;

    // bottom point
    tx = cos(theta)*bottomPoint.x+sin(theta)*bottomPoint.y;
    ty = sin(theta)*bottomPoint.x-cos(theta)*bottomPoint.y;
    bottomPoint.x = tx;
    bottomPoint.y = ty;

    // top and bottom pentagons
    for (int i=0; i<topPent.length; i++){
      tx = cos(theta)*topPent[i].x+sin(theta)*topPent[i].y;
      ty = sin(theta)*topPent[i].x-cos(theta)*topPent[i].y;
      topPent[i].x = tx;
      topPent[i].y = ty;

      tx = cos(theta)*bottomPent[i].x+sin(theta)*bottomPent[i].y;
      ty = sin(theta)*bottomPent[i].x-cos(theta)*bottomPent[i].y;
      bottomPent[i].x = tx;
      bottomPent[i].y = ty;
    }
  }

  void rotX(float theta){
  }

  void rotY(float theta){
  }


}