mathematics – Compensate for gap when rotating plane in a row of planes

I have a row of planes in 3D space that form a road.

Upon rotating a tile around its center point to add a sloap to the road a gap forms like this:
Planes that form a road gap from rotation is shown

To compensate for this gap i developed this formula:

enter image description here

A = (POS - CON)
B = Rot(0, 0, w) * A
C = CON - (POS + B)

POS += C

(All blue values are known)

Please note that the second line resembles a quaternion rotation that rotates vector A by w degrees around an axis through POS leaving your computer screen.

By moving the plane by the calculated amount the gap should be closed (at least as far as I understand) but there is always a small offset:
enter image description here
The offset increases with the rotation angle and gets even worse when the plane is rotated by a rotation not dividable by 90.

Is there a better way to do this or is there something I’m missing with my formula?

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