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Is there an adapter that makes it possible?
Yes
Ta, got a linky?
My Googlefu has only turned up the reverse adaptor
IS to Post mount will help google, assuming by Flat mount you mean IS.
Actually ignore me I’m wrong and full of codiene, sorry.
probably possible but the adapter would need to be pretty awkward.
If you look at this:
[img] 
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you can see how the flat mount is aligned with the fork / stay. To get this alignment on a post mount would need something that offset the caliper and rotated it so it had the same alignment to the axle. I haven't seen such a thing but it may exist
Pretty sure it doesn't exist. I have this issue with my caad 12 disc fork. Why would they make a flat mount rear with post mount front. Had to buy a separate post mount caliper for the front.
Wrong way round Pete.
You CAN adapt flat mount calipers for post mount frames but not the other way round.
+1 (next to) Impossible
There is also the fact that the FM caliper is bolted from the opposite side of the adapter - it has two threaded holes, as opposed to two eyelets in the case of IS and PM calipers.
Why has flat mount come about? Is it for aesthetic reasons on road/gravel bikes? And is it likely to find its way to MTBs?
I've been looking at gravel bikes and I prefer the look of those with flat mounts, I did read a comment that they can cause problems aligning the caliper, whereas post mount is more adjustable?
This was the first result from Google.
[url= http://www.bikehugger.com/posts/road-disc-brake-tech-flat-mount-vs-post-mount/ ]Flat mount versus post mount[/url]
Pretty sure it doesn't exist. I have this issue with my caad 12 disc fork. Why would they make a flat mount rear with post mount front. Had to buy a separate post mount caliper for the front.
Probably because they could only source the fork with post mount.
This is the factor that differentiated between the two final frameset on the shortlist, when I built my road bike, last year.
Didn't want a fugly bodged caliper mounting solution, so went with the frameset that had flat mount front and back.