Rebuilding the Temple

Been thinking about the prophetic events, especially the temple being rebuilt. There are three real parallels between the rebuilding of the second temple with the future third coming temple: 
(1) They are rebuilt by permission and aid of a gentile ruler (Cyrus and the anti-Christ). 
(2) Both temples are built during the period known as the “times of the Gentiles.” [Luke 21:24]. The time from the Babylonian empire and the coming of Christ. 
(3) It is a part of the political decree or covenant made by the gentile ruler and the nation of Israel [Ezra 1:1, Neh. 2;1-9 cf. Dan. 9:27]. This will make the rebuilding of the temple possible.