code: @Override
  	public  Point3d[] getVertices() {
  		double x = getSideLengthFromCircumscribedRadius(circumscribedRadius)/2;
  		double z = x/Math.sqrt(2);
  		Point3d[] tetrahedron = new Point3d[4];
  		tetrahedron[0] = new Point3d(-x,  0, -z);
  		tetrahedron[1] = new Point3d( x,  0, -z);
  		tetrahedron[2] = new Point3d( 0, -x,  z);
  		tetrahedron[3] = new Point3d( 0,  x,  z);
  		Point3d centroid = CalcPoint.centroid(tetrahedron);
  
  		// rotate tetrahedron to align one vertex with the +z axis
  		Matrix3d m = new Matrix3d();
  		m.rotX(0.5 * TETRAHEDRAL_ANGLE);
  		for (Point3d p: tetrahedron) {
  			p.sub(centroid);
  			m.transform(p);
  		}
  		return tetrahedron;
  	}
docs: Returns the vertices of an n-fold polygon of given radius and center
  @param n
  @param radius
  @param center
  @return