Synonyms for Unvarying (same or very similar meaning)
WordNet sense 1 (lacking variety):
unvaried
WordNet sense 2 (persistent in occurrence and unvarying in nature):
changeless, constant, invariant
WordNet sense 3 (not liable to or capable of change):
invariable
WordNet sense 4 (always the same; showing a single form or character in all occurrences):
uniform
From the ODE community, based on WordNet
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