David Tzvi Hoffmann (1969, p. 36, on 1:20, see a recent formulation by Rabbi Jonathan Sacks, 2009, pp. 28,29) notes that the creation of the first day, light, corresponds to the creation on the fourth day, the sun, the moon and the stars. Also, the creation on the second and the fifth days are connected since the animals created on the fifth day, fish and birds, populated the water and air which were formed on the second day. Furthermore, the third and sixth days are also interrelated since the animals and mankind that were created on the sixth day populated the land that was created on the third day.
Cassuto (1883-1951, 1961, pp. 16,17,53) records this same pattern, though he notes that it depends on designating the creation of water or the seas to the second day and not to the third day.
Leo Strauss (lecture in 1957, 1997, pp. 364,365) also notes this pattern. He writes, "There seems to be a kind of parallelism to the biblical account. There are two series of creation, each of three days. The first begins with a creation of light, the second with that of the sun. Both series end with a double creation." Furthermore, he notes a difference between the two sets of creation. He suggests "that the principle of the first half is separation or distinction simply, while the principle of the second half, the fourth to sixth day, is local motion." (Leon Kass, 2003, pp. 27-36, further develops Strauss's ideas with regard to the differences between the two sets.)
Nahum Sarna (1989, p. 4) adds this double creation on days three and six to the pattern from above. He notes that on day three, the two acts of creation, dry land and vegetation, correspond to the two acts of creation on the sixth day, land creatures and humankind. He suggests that vegetation is parallel to humankind since vegetation is the lowest form of organic life while people are the highest form of organic life.
I believe that there is a different literary pattern to the six days of creation. The first day is not part of the parallelism. On day two, the key element was the creation of the rakia, 1:6,7,8, which was populated on the fourth day, 1:14,15,17.
On the third day, the first act of creation was that the land and seas were created, and these were populated on the fifth day by the fish and the birds who would multiply on the land and in the seas, 1:22. Note the Torah relates the birds to the sky in day five, 1:20, and afterwards in 1:26,28,30, which is to be expected, but on day five the crucial aspect is that the birds would populate the land, 1:20,22. The relationship between the birds and land on day five is unexpected and it is not mentioned in day six, but it highlights the connection between the creation on day five and the first act of creation on day three.
The third parallelism is that the second act of creation on the third day was that the vegetation came forth from the earth, 1:12, and similarly, on the sixth day the animals came forth from the earth, 1:24.
With this understanding, mankind, the second act of creation on the sixth day, is outside the parallelism just like the creation of light on the first day is outside the parallelism. Instead, there is a different type of relationship between the creation of light and the creation of mankind. The creation of light started the creation process, while the creation of mankind signaled the end of the creation process.
Overall the pattern of creation is 1, 3, 3, and 1. The first half of creation until the third day has an introduction and three acts of creation, and this is parallel to the second half of creation, the last three days, when there were three corresponding acts of creation and a conclusion. (This numeric pattern is similar to the pattern by the plagues in Egypt; see our discussion, "The ten plagues in Egypt: Their structure, order and maybe their rationale.")
Bibliography:
Cassuto, Umberto (1883-1951), 1961, A commentary on the book of Genesis, part one: From Adam to Noah, Jerusalem: Magnes Press.
Hoffmann, David Tzvi (1843-1921), 1969, Commentary on Genesis, Bnei Brak: Nezach.
Kass, Leon, 2003, The beginning of wisdom, Chicago: University of Chicago Press.
Sacks, Jonathan (1948-2020), 2009, Koren Siddur, Jerusalem: Koren Publishers.
Sarna, Nahum (1923-2005), 1989, The JPS Torah Commentary: Genesis, Philadelphia: The Jewish Publication Society.
Strauss, Leo, 1997, On the interpretation of Genesis, in Jewish Philosophy and the rises of modernity: Essays and lectures in modern Jewish thought by Leo Strauss, edited with an introduction by Kenneth Hart Green, State University of New York Press, pp. 359-376.
Kass, Leon, 2003, The beginning of wisdom, Chicago: University of Chicago Press.
Sacks, Jonathan (1948-2020), 2009, Koren Siddur, Jerusalem: Koren Publishers.
Sarna, Nahum (1923-2005), 1989, The JPS Torah Commentary: Genesis, Philadelphia: The Jewish Publication Society.
Strauss, Leo, 1997, On the interpretation of Genesis, in Jewish Philosophy and the rises of modernity: Essays and lectures in modern Jewish thought by Leo Strauss, edited with an introduction by Kenneth Hart Green, State University of New York Press, pp. 359-376.