Identifying A1 reduction

irrep.jl

@@ -0,0 +1,25 @@
+using DelimitedFiles
+rotations = readdlm("rotations.csv", ',', Int, '\n')
+rotations = reshape(rotations, (24, 3, 3))
+
+N = 24
+ks = -N÷2:N÷2-1
+lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
+labels = reshape(collect(1:N^3), (N, N, N))
+
+for r in 1:24
+    rotated_lattice = Matrix(rotations[r, :, :]) * lattice
+    for index in 1:N^3
+        rotated_lattice_point = rotated_lattice[:, index]
+        (i, j, k) = mod1.(rotated_lattice_point .+ (N÷2 + 1), N)
+        old_label = max(labels[index], labels[i, j, k])
+        new_label = min(labels[index], labels[i, j, k])
+        if old_label != new_label
+            for o in findall(isequal(old_label), labels)
+                labels[o] = new_label
+            end
+        end
+    end
+end
+
+unique(labels)

rotations.csv

@@ -0,0 +1,24 @@
+1,0,0,0,1,0,0,0,1
+1,0,0,0,0,-1,0,1,0
+0,0,1,0,1,0,-1,0,0
+0,-1,0,1,0,0,0,0,1
+1,0,0,0,-1,0,0,0,-1
+-1,0,0,0,1,0,0,0,-1
+-1,0,0,0,-1,0,0,0,1
+1,0,0,0,0,1,0,-1,0
+0,0,-1,0,1,0,1,0,0
+0,1,0,-1,0,0,0,0,1
+0,0,-1,1,0,0,0,-1,0
+0,0,1,-1,0,0,0,-1,0
+0,0,-1,-1,0,0,0,1,0
+0,0,1,1,0,0,0,1,0
+0,1,0,0,0,-1,-1,0,0
+0,-1,0,0,0,-1,1,0,0
+0,-1,0,0,0,1,-1,0,0
+0,1,0,0,0,1,1,0,0
+0,1,0,1,0,0,0,0,-1
+0,-1,0,-1,0,0,0,0,-1
+0,0,1,0,-1,0,1,0,0
+0,0,-1,0,-1,0,-1,0,0
+-1,0,0,0,0,1,0,1,0
+-1,0,0,0,0,-1,0,-1,0