Let us consider the figure given below


Let the height of transmitting antenna or receiving antenna in order to cover the entire surface of earth through communication is $h_t$, and radius of earth is $R$.
Then, maximum distance between $A$ and $B$ is $d_m$ By Pythagoras theorem,
$$
\begin{aligned}
&\mathrm{d}_{\mathrm{m}}^2=\left(\mathrm{R}+\mathrm{h}_{\mathrm{t}}\right)^2+\left(\mathrm{R}+\mathrm{h}_{\mathrm{t}}\right)^2 \\
&=2\left(\mathrm{R}+\mathrm{h}_{\mathrm{t}}\right)^2 \\
&\text { Range of Antenna A and B } \\
&d_m=\sqrt{2 h_t R}+\sqrt{2 h_t R}=2 \sqrt{2 h_t R} \\
&\Rightarrow \quad \mathrm{d}_{\mathrm{m}^2}=4\left(2 \mathrm{Rh}_{\mathrm{t}}\right) \\
&\text { From (i) and (ii), } \\
&\therefore \quad 8 \mathrm{~h}_{\mathrm{t}} \mathrm{R}=2\left(\mathrm{R}+\mathrm{h}_{\mathrm{t}}\right)^2 \\
&\Rightarrow \quad 4 h_t \mathrm{R}=\mathrm{R}^2+2 \mathrm{Rh}_{\mathrm{t}}+\mathrm{h}_{\mathrm{t}}^2 \\
&\Rightarrow \mathrm{R}^2-2 \mathrm{~h}_{\mathrm{t}} \mathrm{R}+\mathrm{h}_{\mathrm{t}}^2=0 \\
&\Rightarrow \quad\left(\mathrm{R}-\mathrm{h}_{\mathrm{t}}\right)^2=0 \\
&\mathrm{R}=\mathrm{h}_{\mathrm{t}} \\
&
\end{aligned}
$$
So the height of Antenna is equal to the radius of earth. Therefore, space wave frequency is used $\lambda \ll \mathrm{h}_{\mathrm{t}}$, hence only tower height is to be taken into consideration. In
three dimensions of earth, 6 antenna towers of each of height $h_t=R$ would be used to cover the entire surface of earth with communication programme.