Question

Why do hexagonal and trigonal lattice do not have bcc and fcc variations?

Answer 1

For trigonal system crystal parameters are given as $a=b=c$ and $\alpha =\beta =\gamma \ne {90}^o$. So, the length of the sides and angles of unit cell are equal but the shape is harder to visualize because $\alpha ,\beta ,\gamma$ can be anything.

For hexagonal system, the crystal parameters are given as $a=b\ne c;\alpha =\beta ={90}^o$ and $\gamma ={120}^o$. So, we have got one restriction to keep $\gamma ={120}^o$

As, in case of the cubic unit cell, we have greater symmetry so we can have bcc and fcc variations but due to lack of such symmetry in trigonal and hexagonal systems we cannot have such variations.