If God, Jesus and the Holy Spirit are co-equal, can you explain the reason why the Holy Spirit doesn't occupy a throne in Revelation 22:1?
"And he showed me a pure river of water of life, clear as crystal, proceeding from the throne of God and of the Lamb" (Revelation 22:1).
People can be equal and yet have different roles to play.
There is only one throne mentioned in Revelation. It is the throne belonging to the Father and the Son. That the Spirit is not mentioned in the particular verse does not tell us anything other than that he was not mentioned. There is nothing in the verse to conclude that it belongs only to the Father and the Son.
But the reason is that the throne is the seat of a ruler's judgment. Throughout the Bible it is mentioned that judgment will be executed by the Son and the Father.
"But we know that the judgment of God is according to truth against those who practice such things. And do you think this, O man, you who judge those practicing such things, and doing the same, that you will escape the judgment of God?" (Romans 2:2-3).
"For the Father judges no one, but has committed all judgment to the Son, that all should honor the Son just as they honor the Father. He who does not honor the Son does not honor the Father who sent Him" (John 5:22-23).
"For we must all appear before the judgment seat of Christ, that each one may receive the things done in the body, according to what he has done, whether good or bad" (II Corinthians 5:10).
The Holy Spirit has been the active person in the Godhead. "The earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the face of the waters" (Genesis 1:2). In Revelation the Spirit is before the throne, a position ready to move and execute decisions. "John, to the seven churches which are in Asia: Grace to you and peace from Him who is and who was and who is to come, and from the seven Spirits who are before His throne, and from Jesus Christ, the faithful witness, the firstborn from the dead, and the ruler over the kings of the earth." (Revelation 1:4). Notice that Revelation is addressed from all three with the Spirit mentioned in the middle.