The words of consecration are “Take this, all of you, and eat it: this is my body which will be given up for you.” The Roman Missal’s rubrics after this are: “He shows the consecrated host to the people, places it on the paten, and genuflects in adoration.”
(Roman Missal, Catholic Book Publishing Co., New York, 1985, pages 545, 549, 552, 558, 1104, 1110-1111, 1116, 1124, 1130; the words of the rubrics are slightly different for the Eucharstic Prayer for Masses with Children II, but the meaning is the same.)
Another time the host is shown, the Roman Missal has:
“The priest genuflects. Taking the host, he raises it slightly over the paten and, facing the people, says aloud:
This is the Lamb of God
who takes away the sins of the world.
Happy are those who are called to his supper.”
The 2002 General Instruction of the Roman Missal also permits holding the consecrated host over the chalice for this prayer:
“84. … The priest next shows the faithful the Eucharistic Bread, holding it above the paten or above the chalice, and invites them to the banquet of Christ.”
And, of course, at communion: “He takes a host for each one, raises it a little, and shows it saying:
The body of Christ.” (Roman Missal, Catholic Book Publishing Co., New York, 1985, page 564.)
For the prayer “Through him, with him, in him …” the priest raises the paten (or plate) with the consecrated host, rather than holding the consecrated host itself.