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The TriangulateMesh command splits all planar quadrangular polygon mesh faces into two triangular mesh faces.
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The TriangulateRenderMeshes command splits all planar quadrangular polygon render mesh faces into two triangular mesh faces.
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Mesh Edit Tools > Triangulate Non‑Planar Quads 
The TriangulateNonPlanarQuads command splits all nonplanar quadrangular polygon mesh faces into two triangular mesh faces.
Options
Any quadrangle where the distance of the quad's fourth point from the plane defined by the quad's first three points is greater than or equal to the Distance value will be triangulated.
Any quadrangle where the angle between the plane normals of the face triangles if it were triangulated is greater than or equal to the Angle value will be triangulated.
Use both distance and angle criteria.
The value by which the Distance and Angle edit boxes are increased or decreased with the spinner controls.
Select a quadrangular mesh face to set the Distance and Angle values.
Divide along the short diagonal.
Divide along the long diagonal.
Minimize resulting area.
Maximize resulting area.
Minimize angle between triangle normals.
Maximize angle between triangle normals.
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The QuadrangulateMesh command merges mesh triangles into quadrangles.
Diagonals that are unwelded (have unique vertexes at the corners) will not be considered as candidates for merging triangles into quadrangles.
Commandline options  

Planarity 
The angle between the face normals of the triangles. 
Rectangularity 
Specify a number greater than or equal to 1. If the adjacent triangles pass the planarity test then they will be merged into a quadrangle if the largest ratio of the lengths of the diagonal is less than or equal to the number you typed, then the triangles are converted to quadrangle. 
Increment 
Increment value used by the spinner controls. 
Rhinoceros 7 © 20102024 Robert McNeel & Associates. 10Apr2024