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The central C atom in the allene molecule is sp hybridised, and the remaining two C atoms are hybridised.
As a result, the central C atom possesses two double bonds, compared to just one double bond for each of the other two C atoms.
On the centre carbon atom, there are two unhybridized, mutually perpendicular p orbitals. Two pi bonds are created between these two unhybridized p orbitals and two nearby C atoms.
As a result, the planes that include the groups are perpendicular to one another.