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The Quadrate Faces command divides all selected triangular faces into four smaller triangular faces by creating three new vertices at the center of each edge. The new vertices are moved outwards to the same radius as the average radius of the vertices of the original faces.
The object illustrated above is an Icosahdron that has been quadrated after selecting all faces. Repeating the quadration of the whole object produces an object that increasingly approximates a sphere.
Only faces that are triangles are quadrated. Quadration of the house, after selecting the whole object, affects only the two triangular faces at each end of the roof ridge.
The term ‘quadration’ is a L3DD invention --- there being no other obvious term for the process.
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