Shelling (topology)

In mathematics, a shelling of a simplicial complex is a way of gluing it together from its maximal simplices (simplices that are not a face of another simplex) in a well-behaved way. A complex admitting a shelling is called shellable.
Definition.
A "d"-dimensional simplicial complex is called pure if its maximal simplices all have dimension "d". Let formula_1 be a finite or countably infinite simplicial complex. An ordering formula_2 of the maximal simplices of formula_1 is a shelling if the complex 
is pure and of dimension formula_5 for all formula_6. That is, the "new" simplex formula_7 meets the previous simplices along some union formula_8 of top-dimensional simplices of the boundary of formula_7. If formula_8 is the entire boundary of formula_7 then formula_7 is called spanning.
For formula_1 not necessarily countable, one can define a shelling as a well-ordering of the maximal simplices of formula_1 having analogous properties.