Crystal structures of famous compounds

Primitive cubic : $O_2,F_2$
Body centred : metals( $Fe,Cr,Mo,W$ ), alkalins ( $Li,Na,K,Cs$ )
Face centred : metals( $Al,Ni,Cu,Ag,Au$ )
Diamond : $C_{diamond},Si,Ge$
Hexagonal close pack : $C_{graphite},N,Se$ metals( $Zn,Cd,Co,Ti$ ), alkalin-earth( $Mg,Be$ ).
Hexagonal 2D : $C_{graphene}$

links

Lattice	number	Space group	Name	Compounds
Monoclinic(1-2)	1	$P1$		$FeS_2$
Triclinic(3-15)	12	$C2m$		$\alpha O_2$
	14	$P2_1/c$		$\alpha Se$
Orthorhombic(16-74)	58	$Pnnm$		$CaCl_2$ , $Fe_2C$
	61	$Pbca$		$Be$ , $CdSb$
Tetragonal(75-142)	139	$I4/mmm$		$In$
Trigonal(143-167)	?
Hexagonal(168-194)	186	$P6_3mc$	Wurtzite	$C_{buckled},GaN$
	191	$P6_3/mmm$	HEX	$H,Li_3N$
	194	$P6_3/mmc$	HCP	$C_{graphite},Zn,Cd,Co,Ti$
Cubic(195-230)	216	$F\bar{4}3m$	Zinblende	$GaAs$
	220	$I43d$		$Li$
	221	$Pm\bar{3}m$	PC	$CsCl$
	225	$Fm\bar{3}m$	FCC	$NaCl$
	227	$Fd\bar{3}m$	Diamond	$C_{diamond},Si,Ge$
	229	$Im\bar{3}m$	BCC	$Fe$

diamond $Si$ space group 227 $Fd\bar{3}m$
zincblende $GaAs$ space group 216 $F\bar{4}3m$ Diamond structure factor : $\begin{equation} F_{hkl} = \left\{ \begin{array}{cc} 8f, & h+k+l=4N \\ 4(1\pm i)f, & h+k+l=2N+1 \\ 0, & h+k+l=4N+2 \end{array}\right. \mbox{,}~~~~~ S_{hkl} = \left\{ \begin{array}{cc} 64f, & h+k+l=4N \\ 32f, & h+k+l=2N+1 \\ 0, & h+k+l=4N+2 \end{array}\right. \end{equation}$

Carbon allotropic forms
- Graphite : Pure carbon forming naturally at SPT
- Diamond : Pure carbon forming under high pressure Gibbs energy formation 0.029eV (12GPa)
- graphene,fullerene : Artificial layered arrangement
Coal : Carbon as extracted, mixed with other compounds
Charcoal : Form of ashes(result of incomplete combustion) of carbon specifically produced from burned wooden logs used as an easy combustible.