There has been a considerable debate about the nature of the short range atomic order in vitreous B(2)O(3). Some authorities state that it is not possible to build a model of glassy boron oxide of the correct density containing a large number of six-membered rings which also fits experimental diffraction data, but recent computer simulations appear to overrule that view. To discover which view is correct I use empirical potential structure refinement (EPSR) on existing neutron and x-ray diffraction data to build two models of vitreous B(2)O(3). One of these consists only of single boron and oxygen atoms arranged in a network to reproduce the diffraction data as closely as possible. This model has less than 10% of boron atoms in boroxol rings. The second model is made up of an equimolar mixture of B(3)O(3) hexagonal ring 'molecules' and BO(3) triangular molecules, with no free boron or oxygen atoms. This second model therefore has 75% of the boron atoms in boroxol rings. It is found that both models give closely similar diffraction patterns, suggesting that the diffraction data in this case are not sensitive to the number of boroxol rings present in the structure. This reinforces recent Raman, ab initio, and NMR claims that the percentage of boroxol rings in this material may be as high as 75%. The findings of this study probably explain why some interpretations based on different simulation techniques only find a small fraction of boroxol rings. The results also highlight the power of EPSR for the extraction of accurate atomistic representations of amorphous structures, provided adequate additional, non-scattering data (such as Raman and NMR in this case) are available.