Peanut/x-shaped features observed in a significant fraction of disk galaxies are thought to have formed from vertically buckled bars. Despite being three-dimensional structures, they are preferentially detected in near edge-on projection. Only a few galaxies are found to have displayed such structures when their disks are relatively face-on - suggesting that either they are generally weak in face-on projection or many may be hidden by the light of their galaxy's face-on disk. Here, we report on three (collisionless) simulated galaxies displaying peanut-shaped structures when their disks are seen both face-on and edge-on - resembling a three-dimensional peanut or dumbbell. Furthermore, these structures are accompanied by ansae and an outer ring at the end of the bar - as seen in real galaxies such as IC 5240. The same set of quantitative parameters used to measure peanut structures in real galaxies has been determined for the simulated galaxies, and a broad agreement is found. In addition, the peanut length grows in tandem with the bar, and is a maximum at half the length of the bar. Beyond the cutoff of these peanut structures, toward the end of the bar, we discover a new positive/negative feature in the B6 radial profile associated with the isophotes of the ansae/ring. Our simulated, self-gravitating, three-dimensional peanut structures display cylindrical rotation even in the near-face-on disk projection. In addition, we report on a kinematic pinch in the velocity map along the bar minor axis, matching that seen in the surface density map.