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.
A d-dimensional simplicial complex is called pure if its maximal simplices all have dimension d. Let
be a finite or countably infinite simplicial complex.
, the complex is pure and of dimension one smaller than
meets the previous simplices along some union
of top-dimensional simplices of the boundary of
not necessarily countable, one can define a shelling as a well-ordering of the maximal simplices of
having analogous properties.