  Honeycomb layered tellurates represent a burgeoning class of multi-functional
materials with fascinating crystal-structural versatility and a rich
composition space. Despite their multifold capabilities, their compositional
diversity remains underexplored due to complexities in experimental design and
syntheses. Thus, in a bid to expand this frontier and derive relevant insights
into allowed metastable compositions, we employ a density functional theory
($\rm DFT$) approach to predict $in$ $silico$ the crystal structures of new
honeycomb layered tellurates embodied by the composition, $A\rm_2 Ni_2TeO_6$
($A$ = alkali, hydrogen or coinage-metal cations). Here, alkali-metal atoms
with vastly larger radii than $\rm K$ ($\rm Rb$ and $\rm Cs$) are found to
engender a prismatic coordination with the oxygen atoms from the honeycomb
slabs whilst coinage-metal atoms ($\rm Ag$, $\rm Au$ and $\rm Cu$) display a
propensity for linear coordination. Further, $\rm H_2 Ni_2TeO_6$ is found to
also render a linear coordination wherein the hydrogen atom preferentially
establishes a stronger coordination with one of the oxygen atoms to form
hydroxyl groups. All $A$ cations in the studied $A\rm_2 Ni_2TeO_6$ compositions
form a honeycomb lattice. Conclusions on the possibility of a monolayer-bilayer
phase transition in coinage metal atom tellurates can be drawn by considering
the implications of conformal symmetry of the cation honeycomb lattice and
metallophilicity. This work not only propounds new honeycomb layered tellurate
compositions but also provides novel insight into the rational design of
multifunctional materials for applications ranging from energy storage,
catalysis and optics to analogue condensed matter systems of gravity.
