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It is easy to set the position of each vertex of a mesh using the SetPositionNode. The change in position is nicely shown in the spreadsheet. The spreadsheet also lists the faces. Is it possible to assign a color depending on the index of the face? What would be the corresponding input node for the face data?

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You can use the Store Named Attribute node and set the domain to Face:

A simple geometry nodes setup coloring each face of the input geometry with a random color based on index as a seed

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