A doctrinaire puzzle with two axes with threefold rotation and heptagonal pieces.

• Inventor: Timur Evbatyrov
• Mechanism: Doctrinaire puzzle with limited axis system
• Patents: Unknown
• Producer: 3D printing service
• Year: 2019
• Original Price: $0.00 USD
• Current Price: No Data

Trientalis was designed to be another twisty puzzle with heptagons. The geometry of this puzzle was discovered by Evgeny Grigoriev a year ago during his investigation of Biaxe-like puzzles and presented in this thread under the name of "Flat Prizm Traheptrix2". It is available in his simulator pcubes.
Trientalis is a deeper-than-origin cut corner turning puzzle with 120-degrees turns about 2 axes. Angles between the axes and faces are set so that the cuts form heptagons and heptagrams on the faces.
Trientalis is a name of a flower which mostly has 7 petals. Having 7-fold rotational symmetry is quite rare for flowers as well as for twisty puzzles.
Despite the heptagons and the odd geometry the puzzle is doctrinaire.

The puzzle has 3590204924839511174676480000000 = 1.23*10^33 permutations if all pieces are considered distinguishable and the orientation of heptagons is visible. Due to the limited number of moves it has a huge number of restrictions:
-The heptagons allow only even permutations.
-The first three heptagons determine the orientation of the fourth.
-The triangles are split into 2 sets of 13 pieces which allow only even permutations.
-The pentagons are split into 2 sets of 7 pieces which allow only even permutations.
-The edges can't be flipped and allow only even permutations.
-The tips are split into 2 sets of three pieces which have only 3 permutations. When one of these 9 permutations is determindes and the orientations of one set then the other orientations are determinded.
-The tips are further restricted by a factor of 3 determined by the permutations of the other pieces.
Stickered as shown here the puzzle has 33398676811019520000000 = 33.4 *10^21 permutations.

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