Cosier had a problem? Solids with twenty faces? (10)

I believe the answer is:

icosahedra

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'solids with twenty faces?' is the definition.
I can't judge whether this definition defines the answer.

'cosier had a problem?' is the wordplay.
'problem?' indicates an anagram (I've seen 'problem' mean this).
'cosier'+'had'+'a'='cosierhada'
'cosierhada' is an anagram of 'ICOSAHEDRA'.

Can you help me to learn more?

(Another definition for icosahedra that I've seen is " They show scores of faces".)

I've seen this clue in the Sydney Morning Herald.

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