The first Append doesn't work, but the second does. The difference is the semicolon. I don't understand this.The problem doesn't depend on Append. The same phenomenon occurs with Union or Insert. I overlook something.
points = {{0, 0, 0}, {1, 1, 0}, {0, 1, 1}, {1, 0, 1}};
In[266]:= pointsums = {}
Out[266]= {}
In[267]:= Append[pointsums, points[[2]]];
In[268]:= pointsums
Out[268]= {}
In[269]:= Append[pointsums, points[[2]]] pointsums
Out[269]= {{1, 1, 0}}
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