<Table> <Tr> <Th> Crystal family </Th> <Th> Crystal system </Th> <Th> Point group / Crystal class </Th> <Th> Schönflies </Th> <Th> Point symmetry </Th> <Th> Order </Th> <Th> Abstract group </Th> </Tr> <Tr> <Td_colspan="2"> triclinic </Td> <Td> triclinic - pedial </Td> <Td> </Td> <Td> enantiomorphic polar </Td> <Td> </Td> <Td> trivial Z 1 (\ displaystyle \ mathbb (Z) _ (1)) </Td> </Tr> <Tr> <Td> triclinic - pinacoidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> </Td> <Td> cyclic Z 2 (\ displaystyle \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td_colspan="2"> monoclinic </Td> <Td> monoclinic - sphenoidal </Td> <Td> </Td> <Td> enantiomorphic polar </Td> <Td> </Td> <Td> cyclic Z 2 (\ displaystyle \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> monoclinic - domatic </Td> <Td> </Td> <Td> polar </Td> <Td> </Td> <Td> cyclic Z 2 (\ displaystyle \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> monoclinic - prismatic </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> </Td> <Td> Klein four V = Z 2 × Z 2 (\ displaystyle \ mathbb (V) = \ mathbb (Z) _ (2) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td_colspan="2"> orthorhombic </Td> <Td> orthorhombic - sphenoidal </Td> <Td> </Td> <Td> enantiomorphic </Td> <Td> </Td> <Td> Klein four V = Z 2 × Z 2 (\ displaystyle \ mathbb (V) = \ mathbb (Z) _ (2) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> orthorhombic - pyramidal </Td> <Td> </Td> <Td> polar </Td> <Td> </Td> <Td> Klein four V = Z 2 × Z 2 (\ displaystyle \ mathbb (V) = \ mathbb (Z) _ (2) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> orthorhombic - bipyramidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 8 </Td> <Td> V × Z 2 (\ displaystyle \ mathbb (V) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td_colspan="2"> tetragonal </Td> <Td> tetragonal - pyramidal </Td> <Td> </Td> <Td> enantiomorphic polar </Td> <Td> </Td> <Td> cyclic Z 4 (\ displaystyle \ mathbb (Z) _ (4)) </Td> </Tr> <Tr> <Td> tetragonal - disphenoidal </Td> <Td> </Td> <Td> non-centrosymmetric </Td> <Td> </Td> <Td> cyclic Z 4 (\ displaystyle \ mathbb (Z) _ (4)) </Td> </Tr> <Tr> <Td> tetragonal - dipyramidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 8 </Td> <Td> Z 4 × Z 2 (\ displaystyle \ mathbb (Z) _ (4) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> tetragonal - trapezoidal </Td> <Td> </Td> <Td> enantiomorphic </Td> <Td> 8 </Td> <Td> dihedral D 8 = Z 4 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (8) = \ mathbb (Z) _ (4) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> ditetragonal - pyramidal </Td> <Td> </Td> <Td> polar </Td> <Td> 8 </Td> <Td> dihedral D 8 = Z 4 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (8) = \ mathbb (Z) _ (4) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> tetragonal - scalenoidal </Td> <Td> </Td> <Td> non-centrosymmetric </Td> <Td> 8 </Td> <Td> dihedral D 8 = Z 4 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (8) = \ mathbb (Z) _ (4) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> ditetragonal - dipyramidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 16 </Td> <Td> D 8 × Z 2 (\ displaystyle \ mathbb (D) _ (8) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> hexagonal </Td> <Td> trigonal </Td> <Td> trigonal - pyramidal </Td> <Td> </Td> <Td> enantiomorphic polar </Td> <Td> </Td> <Td> cyclic Z 3 (\ displaystyle \ mathbb (Z) _ (3)) </Td> </Tr> <Tr> <Td> rhombohedral </Td> <Td> S (C) </Td> <Td> centrosymmetric </Td> <Td> 6 </Td> <Td> cyclic Z 6 = Z 3 × Z 2 (\ displaystyle \ mathbb (Z) _ (6) = \ mathbb (Z) _ (3) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> trigonal - trapezoidal </Td> <Td> </Td> <Td> enantiomorphic </Td> <Td> 6 </Td> <Td> dihedral D 6 = Z 3 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (6) = \ mathbb (Z) _ (3) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> ditrigonal - pyramidal </Td> <Td> </Td> <Td> polar </Td> <Td> 6 </Td> <Td> dihedral D 6 = Z 3 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (6) = \ mathbb (Z) _ (3) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> ditrigonal - scalahedral </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 12 </Td> <Td> dihedral D 12 = Z 6 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (12) = \ mathbb (Z) _ (6) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> hexagonal </Td> <Td> hexagonal - pyramidal </Td> <Td> </Td> <Td> enantiomorphic polar </Td> <Td> 6 </Td> <Td> cyclic Z 6 = Z 3 × Z 2 (\ displaystyle \ mathbb (Z) _ (6) = \ mathbb (Z) _ (3) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> trigonal - dipyramidal </Td> <Td> </Td> <Td> non-centrosymmetric </Td> <Td> 6 </Td> <Td> cyclic Z 6 = Z 3 × Z 2 (\ displaystyle \ mathbb (Z) _ (6) = \ mathbb (Z) _ (3) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> hexagonal - dipyramidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 12 </Td> <Td> Z 6 × Z 2 (\ displaystyle \ mathbb (Z) _ (6) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> hexagonal - trapezoidal </Td> <Td> </Td> <Td> enantiomorphic </Td> <Td> 12 </Td> <Td> dihedral D 12 = Z 6 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (12) = \ mathbb (Z) _ (6) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> dihexagonal - pyramidal </Td> <Td> </Td> <Td> polar </Td> <Td> 12 </Td> <Td> dihedral D 12 = Z 6 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (12) = \ mathbb (Z) _ (6) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> ditrigonal - dipyramidal </Td> <Td> </Td> <Td> non-centrosymmetric </Td> <Td> 12 </Td> <Td> dihedral D 12 = Z 6 ⋊ Z 2 (\ displaystyle \ mathbb (D) _ (12) = \ mathbb (Z) _ (6) \ rtimes \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> dihexagonal - dipyramidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 24 </Td> <Td> D 12 × Z 2 (\ displaystyle \ mathbb (D) _ (12) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td_colspan="2"> cubic </Td> <Td> tetrahedral </Td> <Td> </Td> <Td> enantiomorphic </Td> <Td> 12 </Td> <Td> alternating A 4 (\ displaystyle \ mathbb (A) _ (4)) </Td> </Tr> <Tr> <Td> hextetrahedral </Td> <Td> </Td> <Td> non-centrosymmetric </Td> <Td> 24 </Td> <Td> symmetric S 4 (\ displaystyle \ mathbb (S) _ (4)) </Td> </Tr> <Tr> <Td> diploidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> 24 </Td> <Td> A 4 × Z 2 (\ displaystyle \ mathbb (A) _ (4) \ times \ mathbb (Z) _ (2)) </Td> </Tr> <Tr> <Td> gyroidal </Td> <Td> O </Td> <Td> enantiomorphic </Td> <Td> 24 </Td> <Td> symmetric S 4 (\ displaystyle \ mathbb (S) _ (4)) </Td> </Tr> <Tr> <Td> hexoctahedral </Td> <Td> O </Td> <Td> centrosymmetric </Td> <Td> 48 </Td> <Td> S 4 × Z 2 (\ displaystyle \ mathbb (S) _ (4) \ times \ mathbb (Z) _ (2)) </Td> </Tr> </Table> <Tr> <Th> Crystal family </Th> <Th> Crystal system </Th> <Th> Point group / Crystal class </Th> <Th> Schönflies </Th> <Th> Point symmetry </Th> <Th> Order </Th> <Th> Abstract group </Th> </Tr> <Tr> <Td_colspan="2"> triclinic </Td> <Td> triclinic - pedial </Td> <Td> </Td> <Td> enantiomorphic polar </Td> <Td> </Td> <Td> trivial Z 1 (\ displaystyle \ mathbb (Z) _ (1)) </Td> </Tr> <Tr> <Td> triclinic - pinacoidal </Td> <Td> </Td> <Td> centrosymmetric </Td> <Td> </Td> <Td> cyclic Z 2 (\ displaystyle \ mathbb (Z) _ (2)) </Td> </Tr>

What are the different types of crystal structure