We describe the physical and orbital properties of C/2011 W3. After surviving the perihelion passage, the comet was observed to undergo major physical changes. The permanent loss of the nuclear condensation and the formation of a narrow spine tail was observed first at Malargue, Argentina, on December 20 and then systematically at Siding Spring, Australia. The process of disintegration culminated with an outburst (terminal fragmentation event) on December 17.6 UT. The postperihelion tail, observed for ∼3 months, was the product of activity over <2 days. Because of the delayed response to the hostile environment in the immediate proximity of the Sun, the nucleus' breakup and crumbling was probably caused by thermal stress due to the penetration of intense heat pulse deep into the nucleus' interior after perihelion. The same mechanism may be responsible for cascading fragmentation of sungrazers at large heliocentric distances. The observed behavior is at odds with the rubble-pile model, since the residual mass of the nucleus after perihelion, estimated at ∼10 12 g (a sphere ∼150-200 m across), still possessed significant cohesive strength. The spine tail -the product of the terminal outburst -was a synchronic feature, whose brightest part contained submillimeter-sized dust particles, released at velocities not exceeding 30 m s −1 . The loss of the nuclear condensation prevented an accurate orbital-period determination by traditional techniques. Since the missing nucleus must have been located on the synchrone, whose orientation and sunward tip have been measured, we compute the astrometric positions of this missing nucleus as the coordinates of the points of intersection of the spine tail's axis with the lines of forced orbital-period variation, derived from the orbital solutions based on high-quality preperihelion astrometry from the ground. The resulting orbit gives 698 ± 2 years for the osculating orbital period, which proves that C/2011 W3 is the first major member of the expected new, 21st-century cluster of bright Kreutz-system sungrazers, whose existence was predicted by these authors in 2007. From the spine tail's evolution, we determine that its measured tip, populated by dust particles 1-2 mm in diameter, receded antisunward from the computed position of the missing nucleus. The bizarre appearance of the comet's dust tail in images taken only hours after perihelion with the coronagraphs on board the SOHO and STEREO spacecraft is readily understood. The disconnection of the comet's head from the tail released before perihelion and an apparent activity attenuation near perihelion have a common cause -sublimation of all dust at heliocentric distances smaller than about 1.8 solar radii. The tail's brightness is strongly affected by forward scattering of sunlight by dust. From an initially broad range of particle sizes, the grains that were imaged the longest had a radiation-pressure parameter β ≃ 0.6, diagnostic of submicron-sized silicate grains and consistent with the existence of the dust-free zone around ...