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That tensile hoop stresses will cause an un-chained masonry dome to burst is well known, but the stabilizing influence of hoop-wise compression is rarely discussed. An arch cannot exhibit hoop stresses of any kind, so freestanding masonry arches must fit their own funiculars. But hoop compression does arise in some domes, such as those designed on shallow circular arcs. And as long as the hoop stresses they develop are exclusively compressive (except, of course, at the base), masonry domes are free to take certain non-funicular forms. To explore this design freedom, the author and his students built an unusual array of domes of un-bound and un-mortared masonry. Notable examples include the anticlastic or bell-shaped roofs we call pseudomes, some antidomes that descend from their foundation ring to form basins, and a hemi-toroidal ambidome that rises conventionally from its foundation to a circular crown whence it descends to a pendant oculus. To the best of our knowledge, the anti- and ambidomes are unprecedented in the history and theory of structures. The material success of these counterintuitive structures advanced our understanding of masonry, it raised some questions about the natural and the artificial in structural form-finding, and it challenged our preconceptions about the optimal, the ideal, and the free in structural form. [ABSTRACT FROM AUTHOR]