We all know what a cross looks like, and yet when asked to describe one, the only valid answer is, "Which one?"
Or more cryptically, "When is a cross not a cross?" to which there are a surprising number of possible answers. These include war memorials, various stars, and hundreds of others you can see on our cross index. This page shows another non-cross cross, the Crux Simplex. (Also known as a Stipe, Pole, Post, Stake, etc., or even a Phallic Symbol!)
The Crux Simplex or Stipe, being a simple upright post, does not have the transverse beam found on other forms.
The post can, if we wish, have phallic symbolism, and from a Christian perspective, it could be said that this does reinforce the concept of "new life". However, it is more likely that such associations are little more than sophistry, pareidolia, phallophilia, some other fancy word. All of which are simply a distraction from considering the infinitely more important symbolism of the Cross.
The ancient Greek word for stake is stauros (n) and stauroo (v). This simple post was common for crucifixions until the Phoenicians added a cross beam.
The Crux Simplex evolved from a tree (an infelix lignum or an arbor infelix) dedicated to the gods of the nether world. Such trees are non-fruiting, unproductive, valueless, and therefore considered appropriate to use in crucifying criminals.
Historians and etymologists have debated whether the scaffold in early Scriptures meant Jesus was executed on a simple upright post, or a post with a cross beam (either a ✞ shaped Latin Cross, a 'Y' shaped Forked Cross, an 'X' shaped St. Andrew's Cross or a 'T' shaped Tau Cross). The common belief is that it was not a simple upright post, but the distinction is nowhere nearly as important as the reason why Jesus was executed.
The Bible says that Jesus was hung on a tree. Whether it was an actual rooted tree or an upright wooden post set into the ground (see Broken Cross), the common consensus is that a transverse beam (patibulum) was then added. A usual crucifixion method was to bind the condemned person's wrists to a beam and then attach that beam to a tree or stipe, thereby forming a cross (crux composita or crux acuta).
The Greeks apparently used the word 'stauros' to represent a wide range of wooden structures used for executions, but Jehovah's Witnesses and a few others interpret the word to mean Jesus was executed on a post without a patibulum.
This is not a moot point. Hanging with the arms above the head ensures the victim suffocates and dies quickly. This was not desired by the soldiers, who wanted to stretch the consciousness and suffering until sundown. Neither does a swift death with minimal suffering fit Christian theology. Jesus was crucified in the most painful and agonising way that our sins might be forgiven. See Why Jesus Died.