figure eight vs plane figure

figure eight and plane figure both are nouns.

Word	Noun	Adjective	Verb	Adverb
figure eight	Yes	No	No	No
plane figure	Yes	No	No	No

As nouns, plane figure is a hypernym of figure eight; that is, plane figure is a word with a broader meaning than figure eight:

Other hypernyms of figure eight include two-dimensional figure.

figure eight (noun)	plane figure (noun)
a skating figure that carves an 8 in the ice	a two-dimensional shape
a knot having the shape of the numeral 8; tied in a rope that has been passed through a hole or pulley and that prevents the rope from coming loose
a two-dimensional figure having the shape of the number eight