What are the three geometric isomers of dibenzalacetone?

Dibenzalacetone (trans, trans-1,5-diphenylpenta-1,4-dien-3-one) is prepared by the aldol condensation of acetone with excess benzaldehyde.

Initially, one mole of benzaldehyde reacts with one mole of acetone to form benzylidineacetone (4-phenylbut-3-en-2-one)

#"C"_6"H"_5"CHO" + "CH"_3"COCH"_3 stackrelcolor(blue)("NaOH"color(white)(m))(→) underbrace("C"_6"H"_5"CH=CHCOCH"_3)_color(red)("benzylidineacetone") + "H"_2"O"#

This newly-formed ketone still possesses alpha hydrogens, so it can undergo another aldol condensation with a second mole of benzaldehyde:

#underbrace("C"_6"H"_5"CH=CHCOCH"_3)_color(red)("benzylidineacetone")+ "CH"_3"COCH"_3 stackrelcolor(blue)("NaOH"color(white)(m))(→) underbrace("C"_6"H"_5"CH=CHCOCH=CHC"_6"H"_5)_color(red)("dibenzalacetone") + "H"_2"O"#

You can have cis-trans isomerism about each of the double bonds.

The possible combinations are cis,cis, cis,trans, trans,cis, and trans,trans.

The cis,trans and the trans,cis forms, however, are identical, so there are only three isomers.