The most common and most likely answer to this crossword clue is the 8 letter word MONUMENT
M
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More clues leading to the result MONUMENT
- Greek character in short time creates shrine
- Greek character buried in second tomb
- Memorial has significance probed by character abroad
- Greek character features in second statue maybe
- Second collection of teachers surrounding fellows in Tube station
- Importance shrouding Greek character’s memorial
- Shake fan, welcoming soldiers in memorial building
- Statue half nude, coming in second
- Flash around half naked statue
- Men mount awkwardly on memorial
Buddy explains!

The straight part
We know that "Edifice" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case edifice = monument.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.
What does MONUMENT mean?
MONUMENT noun- A structure built for commemorative or symbolic reasons, or as a memorial; a commemoration.
- An important site owned by the community as a whole.
- An exceptional or proud achievement.
- An important burial vault or tomb.
- A legal document.
- A surveying reference point marked by a permanently fixed marker (a survey monument).
- A pile of stones left by a prospector to claim ownership of ore etc. found in a mine.
- To mark or memorialize with a monument.