Gallery
Discrete minimal surfaces
The figure below shows a small part of a discrete Ennerper surface. Its faces are all planar, hexagonal and noncovex (because of negative Gaussian curvature).
Associated family of minimal surfaces
The above shows a family of surfaces with planar faces. Their corresponding edges are parallel but lengths are changing. On every face, the integrated mean curvature vanishes.
W. Y. Lam. Discrete minimal surfaces: critical points of the area functional from integrable systems (2015). arXiv: 1510.08788.
Circle patterns from bipartite graphs
A biparite graph is immersed in the plane with cyclic faces, which yields a circle pattern. The dual graph is embeded as the centers of the circles. Fixing the centers, the red vertex can be moved around to obtain a 2-parameter family of circle patterns. One can try it in the Geogebra applet.
More details are in Dimers and Circle patterns. (2018). arXiv: 1810.05616