The most common and most likely answer to this crossword clue is the 5 plus 6 letter word KLEIN BOTTLE
I've seen this crossword clue in The Times
K
L
E
I
N
B
O
T
T
L
E
Buddy explains!
The straight part
We know that "four-dimensional concept" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case four-dimensional concept = klein bottle.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.