Before revision:  The proposed online algorithm of Chen et al. is upper-bounded by 5.99  , which is achieved by considering a circumscribed dodecahedron followed by a recursive decomposition of each face.
After revision:  The proposed online algorithm of Chen et al. is upper-bounded by 5.99 and later improved to 3.69 , which is achieved by considering a circumscribed dodecahedron followed by a recursive decomposition of each face.