The ND patch is a play off of what the Armored Divisions did with the triangle further broken up into three colors. Those patches are all similar, in the fact that they are triangles, but they have different symbols inside, one has a track to signify the armored division, another had a lightning bolt or something. I donno much about them, nor was I stationed with any armored units. I was light infantry.
With none so fair that they can compaaaaaaaaare, to the airborne infantry ah ha.
The football team should never get to wear that, unless they are honoring troops, or more pointedly, their classmates who made the commitment to their country. That's the only way I'd go for it, and I don't think it'd happen anyway.