A chord diagram is a degree three graph with a designated outer circle. It looks like a circle with lines going across it. The intersection graph of a chord diagram is a graph that shows how the lines inside the circle cross each other. Many chord diagrams can share an intersection graph. The intersection graph conjecture asks, “If two chord diagrams share an intersection graph are they equal for a sense of equality of chord diagrams?” I found a new family of intersection graphs for which the answer to this question is “yes.” I have included some artwork that I produced while discovering this result.