|(photo credit Conor Hogan, 2014)|
"Halo" comes from the Greek ἅλως, which means the "shining disk" of the sun or moon.* There have been many representations of haloes in art throughout the whole of art history. Sometimes they are represented as rays shining out from the head of a special person. Often they are circular. The circle may be portrayed as a disk behind the saint's head, looking like a large dinner plate floating so that his or her head is perfectly centered in the circle. In the Renaissance (see the top image here), when realistic perspective became a goal in art, the halo was often shown as if it were a perfectly round and flat disc that was attached to the back of the head, so that at an angle you would see it as an elliptical hat (check out the fancy hats here). Later, it was fashionable to portray it as a simple lighted "hoop," as we see in this 15th-century painting.
There were some special haloes, used in only certain circumstances. Members of the Holy Trinity could be seen with a halo that had three rays (or sets of three lines) extending from the head to the circumference. We see that in the diagram to the right. A halo made of stars was used only for the Blessed Virgin Mary (here is a sample, connecting her to the EU flag), because of the woman whose head was surrounded by 12 stars mentioned in the Book of Revelation who gives birth to the child who was to rule all nations.
Which leaves the triangle. The triangle also represented the Trinity, but was used solely for depicting God the Father. This was perhaps because the triangle is the obvious symbol for the Trinity. It could be because God the Father rules in Heaven, and "heaven" or the area above the earth was sometimes represented symbolically as a triangle. Earth's symbol was a square, due to the four cardinal directions and the "four corners of the earth," and if you look from one horizon to straight up and then down to the far horizon, you have drawn a triangle with your eyes.
So, the church in Lackawanna, NY, drew from some old symbolism for the depiction of God on the dome; clearly, it was not built by iconoclasts.
*You can see examples of the meteorological phenomena that inspired the word here.