Bygride-3-3-4 with different cutting depths.

• Inventor: Linxiao Xu
• Mechanism: Doctrinaire puzzle with limited axis system
• Patents: Unknown
• Producer: Customly 3D printed
• Year: 2021
• Original Price: $0.00 USD
• Current Price: No Data

This puzzle is designed by adding one more 3-fold axis to Bram's Sphere Inverted (see the separate entry), transforming it to the shape of the Heartrix (see the separate entry), and then adjusting its cut depth to hide the centres of the two 3-fold axes. Phrased differently, the puzzle could be seen as a truncated tetragonal trapezohedron with one 4-sided corner and two 3-sided corners that can be turned. The 4-sided corner turn is a deeper-than-origin cut.
Another relative is the TriQuad. Compared with that Heartrix adds another axis.
Like the Heartrix it has two axes with 120� turns and one axis with 90� turns. Unlike the Heartrix the cuttings depths are totally different.
The inventor was fascinated by the thread "Making non-jumbling puzzles great again" and all the puzzles the discussions led to. In early 2019, he wrote a post on mf8 forum to introduce those concepts and puzzles to Chinese cubers. Two years later he came up with the Heatrix Inverted and decided to print it out.
A standard two-shell mechanism is used. Unfortunately he forgot to add tolerance to some faces, so he had to do some extra sanding work to make it playable.
Edge length (short edges of the underlying tetragonal trapezohedron): 38 mm
Weight: 92 grams

The puzzle has 3590204924839511174676480000000 = 1.23*10^33 permutations if all pieces are considered distinguishable. Due to the limited number of moves it has a huge number of restrictions:
-The orientation of the sixth corners is determined by the other five.
-The edges can't be flipped.
-The edges have even permutations.
-The permutation of the corners and the orientation of the square tip have the same parity.
-The permutation of the triangles and the orientation of the square tip have the same parity.
-The permutation of the trapeziums and the orientation of the square tip have the same parity.
Stickered as shown here the puzzle has 33398676811019520000000 = 33.4 *10^21 permutations.

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