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I need to rotate the object around its center to align to the average between the 2 faces on either side. I found this answer which is absolutely what I want to do but to no avail. Really I need is a flat side pointing up (not the corner)

This is exactly what I want to achieve but can not find the correct solution Geometry node - instantiating a cube only in the middle of another geometry edge

Flat sides need to face up

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you can try this node setup:

enter image description here

result:

enter image description here

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Not necessarily the right way for you to go... (this illustration leaves out other aspects, scaling by edge-length, etc.,) ... but if your reference geometry has faces, a Normal in the Edge domain is the average of the normals of adjacent faces.

enter image description here

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