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An algorithm to cycle 3 triangular pieces is:
2R 2L' 2R' 2L u 2L' 2R 2L 2R' 2u' 2R 2L' 2R' 2L u 2L' 2R 2L 2R'
(lowercase indicates slice moves)
I hope this is useful.
-Mark-

which triangle piece anyway? the obtuse triangle piece or the acute triangle piece?