Symmetric 5-neighbor [2D cellular automaton] rules

Among the 32 possible 5-cell neighborhoods shown for example on page 941 there are 12 classes related by symmetries, given by

s = {{1}, {2, 3, 9, 17}, {4, 10, 19, 25}, {5}, {6, 7, 13, 21}, {8, 14, 23, 29}, {11, 18}, {12, 20, 26, 27}, {15, 22}, {16, 24, 30, 31}, {28}, {32}}

Completely symmetric 5-neighbor rules can be numbered from 0 to 4095, with each digit specifying the new color of the cell for each of these symmetry classes of neighborhoods. Such rule numbers can be converted to general form using

FromDigits[Map[Last, Sort[Flatten[Map[Thread, Thread[{s, IntegerDigits[n, 2, 12]}]], 1]]], 2]