B2 abstract crystals having a modified regular tetrahedron shape are provided crystals preferably have four substantially identical triangular faces that define four truncated vertices and six chamfered edges the six chamfered edges can have an average length of l and an average width of w and 8 u2266 l w u2266 9 5 application_number US 201514640146 A description the following discussion provides many example embodiments of the inventive subject matter although each embodiment represents a single combination of inventive elements the inventive subject matter is considered to include all possible combinations of the disclosed elements thus if one embodiment comprises elements a b and c and a second embodiment comprises elements b and d then the inventive subject matter is also considered to include other remaining combinations of a b c or d even if not explicitly disclosed the inventive subject matter provides compositions and methods in which a piezoelectric hydrothermally grown synthetic quartz crystal is precision cut to form a tetrahedron that is perfectly aligned with the molecular structure of the quartz crystal along the z or c and x axes the quartz should be crystalline and include no fused or amorphous silica sio 2 or substantially no fused or amorphous silica sio 2 viewed from a different perspective the alignment is preferably within one degree of the arc in both the z and x axes crystals of the inventive subject matter are preferably cut to accord with geometric equations in preferred embodiments the uncut edge of the starting tetrahedron.