In mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toric variety constructed by applying the hyper-Kähler quotient construction of N. J. Hitchin, A. Karlhede, and U. Lindström et al. (1987) to a torus acting on a quaternionic vector space. Roger Bielawski and Andrew S. Dancer (2000) gave a systematic description of hypertoric varieties.

• Bielawski, Roger; Dancer, Andrew S. (2000), "The geometry and topology of toric hyperkähler manifolds" (PDF), Communications in Analysis and Geometry, 8 (4): 727–760, doi:10.4310/CAG.2000.v8.n4.a2, MR 1792372
• Hitchin, N. J.; Karlhede, A.; Lindström, U.; Roček, M. (1987), "Hyper-Kähler metrics and supersymmetry", Communications in Mathematical Physics, 108 (4): 535–589, doi:10.1007/BF01214418, MR 0877637, S2CID 120041594