Naturally occurring proteins vary the precise geometries of structural elements to create distinct shapes optimal for function. We present a computational design method, loop-helix-loop unit combinatorial sampling (LUCS), that mimics nature's ability to create families of proteins with the same overall fold but precisely tunable geometries. Through near-exhaustive sampling of loop-helix-loop elements, LUCS generates highly diverse geometries encompassing those found in nature but also surpassing known structure space. Biophysical characterization showed that 17 (38%) of 45 tested LUCS designs encompassing two different structural topologies were well folded, including 16 with designed non-native geometries. Four experimentally solved structures closely matched the designs. LUCS greatly expands the designable structure space and offers a new paradigm for designing proteins with tunable geometries that may be customizable for novel functions.