The Collaborative International Dictionary of English v.0.48:

Regularity \Reg`u*lar"i*ty\ (-l?r"?*t?), n. [Cf. F.
   r['e]gularit['e].]
   The condition or quality of being regular; as, regularity of
   outline; the regularity of motion.
   [1913 Webster]

WordNet (r) 3.0 (2006):

regularity
    n 1: a property of polygons: the property of having equal sides
         and equal angles [syn: regularity, geometrical
         regularity]
    2: the quality of being characterized by a fixed principle or
       rate; "he was famous for the regularity of his habits" [ant:
       irregularity, unregularity]

Moby Thesaurus II by Grady Ward, 1.0:

125 Moby Thesaurus words for "regularity":
   arrangement, array, balance, bilateral symmetry, cadence,
   ceaselessness, chattering, clockwork regularity, concord,
   conformity, congruity, consistency, constancy, constant flow,
   continualness, continuity, correspondence, daily round,
   dependability, deployment, dingdong, disposal, disposition,
   downiness, drone, dynamic symmetry, equality, equilibrium,
   eurythmics, eurythmy, even pace, even tenor, evenness, finish,
   flatness, formation, frictionlessness, glabriety, glabrousness,
   glossiness, greasiness, harmoniousness, harmony, health,
   incessancy, invariability, keeping, layout, levelness, lineup,
   lubricity, marshaling, monologue, monotone, monotonousness,
   monotony, multilateral symmetry, naturalism, naturalness, naturism,
   noninterruption, normalcy, normality, normalness, oiliness, order,
   orderliness, organization, oscillation, pace, parallelism, peace,
   perpetuity, polarity, predictability, proportion, proportionality,
   propriety, pulsation, quick fire, quiet, quietude, rapid fire,
   rapid recurrence, rapid succession, rapidity, realism, reliability,
   repetition, rhythm, routine, sameliness, sameness, satininess,
   setup, shapeliness, silkiness, singsong, sleekness, slickness,
   slipperiness, smoothness, stability, staccato, steadiness,
   structure, stuttering, suavity, sustainment, symmetricalness,
   symmetry, system, tattoo, tranquillity, treadmill,
   trilateral symmetry, undeviation, undifferentiation, uniformity,
   unintermission, uninterruption, unvariation, velvetiness,
   vibration, wholesomeness