Yes. Crucifix means to fasten to something. Prometheus, for example, was crucified; fastened to the ground or rock. Jesus was crucified (fastened) to an upright pole. The Hebrew torture stake. Single piece. The Greek word used is stauros, which can mean an upright pole or any variation of a cross. The T shaped Tau from Tammuz, the X shaped cross, other shapes. The cross goes back long before Jesus. It was used as a fertility symbol like the ichthys
(fish) symbol also used later by Pagan/Christians and the Pentagram.
The thing is, during Jesus' time the Romans were doing a lot of crucifying in an arid climate without many trees. Why use more wood than was needed. Just one piece. Though the Greek word stauros can mean a pole or various shaped cross, the Greek word xylon, which was also used to describe what Jesus died upon, was also used and can only mean a single upright pole, timber or tree. For example, the LXX translates xylon from the
Hebrew at
Ezra 6:11. (Luke 23:31; Acts 5:30; 10:39) Jesus didn't die on a t shaped cross.