Male doctor within hearing two-faced? Three! (9)

I believe the answer is:

trihedral

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'two-faced? three' is the definition.
The definition suggests a singular noun which matches the answer.

'male doctor within hearing' is the wordplay.
'male' becomes 'he' (he refers to a man).
'doctor' becomes 'Dr' (abbreviation).
'within' indicates putting letters inside.
'hearing' becomes 'trial' (I've seen this in another clue).
'he'+'dr'='hedr'
'hedr' put into 'trial' is 'TRIHEDRAL'.

Can you help me to learn more?

(Other definitions for trihedral that I've seen before include "presenting a number of faces" , "Having three faces" , "having three planes" , "on more than two sides" .)

I've seen this clue in The Independent.

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