It is known that allene (propadiene) $\ce{H2C=C=CH2}$ geometry is such that its hydrogen atoms are not in the same plane – do not form rectangle, but “extended tetrahedron”

allene structure

I wonder if structurally analogous carbon dioxide $\ce{O=C=O}$ exhibit similar geometry, i.e. do its lone electron pair orbitals form extended tetrahedron as well (IUPAC officers probably would not like following structure diagram)

enter image description here

or are they in the same plane? And why?