I have computed some equations of algebraic quartic surfaces with rational double points.
More precisely, all possibilities with total Milnor number 19 which have no singularity of type A_n.
Magma code for 'On the computation of singular plane curves and quartic surfaces' here.
The images below were obtained with the software
Surfer.
E7E6D6
E7D12
E6E8D5
E6E6D7
E6D13
E6D8D5
D18A1
D7D6D6
