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The word translated cross in the New Testament is the Greek noun ‘stauros’ – meaning literally a stake - from a verb meaning ‘to stand’.
Crucifixion certainly involved an upright stake fastened into the ground. As it is unlikely that the condemned could have borne the weight of this, the general inference is that what the condemned carried was a stake which formed a crosspiece which would be fastened to the upright stake.
The word translated ‘crucify’ is ‘stauroo’ meaning literally to ‘stake’ that is - to fasten to a stake.
From the Bible itself the shape of the cross cannot be determined. The crucifixion was foretold in Psalm 22:
Psalms 22:16 For dogs have surrounded Me; The congregation of the wicked has enclosed Me. They pierced My hands and My feet;
The point of the crucifixion is not the shape but that by being fastened to a stake of wood the sinless Christ was brought under the curse of the Law of Moses.
Deuteronomy 21:22 If a man has committed a sin deserving of death, and he is put to death, and you hang him on a tree, 23 "his body shall not remain overnight on the tree, but you shall surely bury him that day, so that you do not defile the land which the LORD your God is giving you as an inheritance; for he who is hanged is accursed of God.
The hanging of Christ on a stake or cross of wood was necessary to show that, in raising him from the dead, God has put aside the Law of Moses.
Galatians 3:13 Christ has redeemed us from the curse of the law, having become a curse for us (for it is written, "Cursed is everyone who hangs on a tree"),