When constructing mapping class group-equivariant cell decompositions of Teichmueller space, the theory is greatly simplified by the existence of punctures or at least marked points, relative to which it is possible to construct cell decompositions. Two people who have independently pioneered the study of mapping class group-equivariant cell decompositions of Teichmueller space of closed compact surfaces without marked points are Schmutz and Thurston. In this talk it will be shown that a special case of Schmutz's construction can be understood to be dual to a mapping class group-equivariant spine constructed by Thurston.