[Cronos]

question: wasn’t the third temple the one built by Herod the Great? The first by Solomon, the second rebuilt after the exile and the third by Herod?

[Former Fetus]

wasn’t the third temple the one built by Herod the Great?

Good question! Actually Herod's Temple was a renovation/expansion of the Temple built by the Jews returning from Babylon, so it is still considered to be the second Temple.

[Lera]

question: wasn’t the third temple the one built by Herod the Great? The first by Solomon, the second rebuilt after the exile and the third by Herod?

Not exactly , Herod just remodeled the second Temple that Zerubbabel built after Darius gave Nehemiah the edict to rebuild the walls of Jerusalem . That is only two Temples , Solomon's , Zerubbabel's and Herod's remodel of the Temple built by Zerubbabel.

There will be a third Temple because we know that the Antichrist will desecrate it in the middle of the tribulation period just like Antiochus Epiphanes did .

Antiochus Epiphanes is a proto type of antichrist , and his desecration of the Temple was only a partial fulfilment.