These puzzles are tetrahedral with edge turns. Puzzles Te3 and Te4 in this series have extra moves if you remove the restriction that they must be tetrahedral, since in fact they can be considered as shape modifications of the 3x3x3 and 2x2x2 Rubik's Cube.
 Puzzle Te1: Gelatinbrain Number: n/a Common Name: n/a Types of Pieces: 4 fixed centers, 6 trivial edges, 12 centers in 3 orbits, 4 corners. Solution: Solve the edges by twisting them in place. The centers can then be solved with fourmove commutators of adjacent edges. Finally the corners can be solved with commutators of the form (DL) (DU DR DU DR) (DL)' (DU DR DU DR)'.

 Puzzle Te2: Gelatinbrain Number: 5.2.1 Common Name: Senior Pyraminx (?) Types of Pieces: 6 trivial edges, 12 centers in 3 orbits, 4 corners. Solution: Solve the edges by twisting them in place. The centers can then be solved with fourmove commutators of adjacent edges. Finally the corners can be solved with commutators of the form (DL) (DU DR DU DR) (DL)' (DU DR DU DR)'. 
 Puzzle Te3: Gelatinbrain Number: 5.2.3 Common Name: Mastermorphix (half turns only) Types of Pieces: 6 trivial edges, 4 corners, 4 triangular centers, 12 trapezoidal centers in 3 orbits. Solution: Solve the edges by turning them in place. Solve one triangular center and one adjacent corner using fourmove commutators of adjacent edge turns, then solve the rest of the triangular centers and corners (and the edges) by alternating the two turns which do not disturb the two that were solved before. Finally the trapezoidal centers can all be solved with commutators of the form (DL) (DU DR DU) (DL)' (DU DR DU)'. 
 Puzzle Te4: Gelatinbrain Number: n/a Common Name: Pyramorphix (half turns only) Types of Pieces: 4 corners, 4 centers. Solution: First pair up one corner with one center. Then there are only two possible moves which do not break up this pair; alternate between them until the puzzle is solved.

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