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Tetragram
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Four axes and four effective sides with the cutting pattern of a Starminx II.

This puzzle was first conceived in 2015 but physically implemented for the first time four years later. It was designed to occupy a place between Krystian's Twist and the Starminx II. All three share the same appearance of cutting patterns and all three are edge turning and allow jumbling.
Unlike its sibling the Tetragram allows turning on four axes.
The shape has 10 faces, 2 squares of unequal size, 4 pentagons, and 4 right isoceles triangles. Stickers were cut by Jason Gavril.
Solving must be highly unusual because the triangles are split in sets of 5 that share the same orbits. The top and bottom edges are split in stes of 3 that share the same orbits.
Edge length (long): 63 mm
Edge length (short): 45 mm

The puzzle has 25194240000000 = 25.2*10^12 permutations if all pieces are considered distinguishable.
Compared with the number available if the puzzle can be disassembled and reassembled there are these restrictions:
-The asymmetric edges are split into 4 sets.
-The combined permutation of the asymmetric edges is always even.
-The parity of the first three sets of asymmetric edges is determined by the parity of the symmetrical edges.
-The triangles are split into 3 sets.
-Only the first set of triangles can be permuted completely. For the other three sets the last two triangles can't be permuted freely.
-The parity of the first set of triangles derives from the orientation of then symmetrical edges.
-The orientation of the last pentagon is determined by the other three.
-The parity of the pentagons ist identical to parity of the symmetrical edges.
Stickered as shown here the puzzle has 201553920000 = 202*10^9 permutations.


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