Potassium hexachloroplatinate $(K_2PtCl_6)$ adopts an antifluorite crystal structure. The corners and face centers of the cubic unit cell are occupied by :-

$A$ two-dimensional solid is made by alternating circles with radius $a$ and $b$ such that the sides of the circles touch. The packing fraction is defined as the ratio of the area under the circles to the area under the rectangle with sides of length $x$ and $y$. The ratio $r=b/a$ for which the packing fraction is minimised is closest to $.....$

$A$ body-centred cubic $(BCC)$ lattice is made up of two different types of atoms $X$ and $Y$. Atom $X$ occupies the body centre and atoms $Y$ occupy the corner positions. One of the corners is left unoccupied per unit cell. The empirical formula of it is

The arrangement $ABC ABC ABC …..$ is referred to as:

An alloy of metals $A$,$B$,and $C$ is found to have $A$ constituting a $ccp$ lattice. If $B$ atoms occupy the edge centers and $C$ is present at the body center,the formula of the alloy is:

The number of octahedral and tetrahedral holes respectively present in a hexagonal close packed $(hcp)$ crystal of $X$ atoms are