This is an animation of the Pansu-Wulff shape in the Heisenberg group with the sub-Finsler structure associated to an equilateral triangle. Since the triangle is not centrally symmetric, the shape is not symmetric with respect to a horizontal plane
Geometric properties of these shapes may be found in a recent paper by J. Pozuelo and M. Ritoré posted in arXiv:2007.04683.