Duality and Triality Families of Analytic Black Hole Solutions

Recent progress in holographic realization of strange metal transport has given us new insights into getting new black hole solutions. In this paper, we consider the $S$-completion and $ST$-completion of the Gubser-Rocha model. The dyonic black holes of the S-type Gubser-Rocha model come in families as ${\mathbb{Z}}_4$ quartets. For the $ST$-completion, solutions form sextets under ${\mathbb{Z}}_6$ symmetry. The charge vectors of the solutions in each ${\mathbb{Z}}_6$-family form a hexagon, realizing six-fold way in gravitational systems.