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Cubic
a=b=c
alpha=beta=gamma= 90
Hexagonal
a=b but NOT=c
alpha=beta=90
gamma=120
Trigonal
a=b=c
alpha=beta=gamma BUT NOT 90,
tetragonal
a=b but NOT =c
alpha=beta=gamma=90
orthorhombic
a NOT EQUAL b NOT EQUAL c
alpha=beta=gamma=90
monoclinic
a NOT EQUAL b NOT EQUAL c
alpha=gamma=90
BUT NOT=beta
triclinic
a NOT EQUAL b NOT EQUAL c
alpha NOT EQUAL beta NOT EQUAL gamma
Equal sides a=b=c
Cubic, Trigonal
Unequal side a not= b not=c
Triclinic, Monoclinic, Orthorombic
a=b BUT NOT c
Hexagonal, Tetragonal
All angles are 90
Cubic, Trigonal, Orthorombic