Solid figures that could be tidier with a corset – ah! (15)

I believe the answer is:

icositetrahedra

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'solid figures' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'could be tidier with a corset ah' is the wordplay.
'could be' indicates anagramming the letters.
'with' says to put letters next to each other.
'tidier'+'a'+'corset'+'ah'='tidieracorsetah'
'tidieracorsetah' anagrammed gives 'ICOSITETRAHEDRA'.

'that' acts as a link.

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I've seen this clue in The Guardian.

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