The most common and most likely answer to this crossword clue is the 8 letter word COPLANAR
I've seen this crossword clue in The Times
C
O
P
L
A
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The straight part
We know that "on the same flat surface" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on the same flat surface = coplanar.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
COPLANAR adjective- (of at least two things, usually lines or plane figures) Within the same plane.
- (of multiple planets or other orbiting bodies) Orbiting a central celestial object within the same orbital plane.