Today, I also decided upon the chapter's icon. The original planetary defense force for which this chapter gets its members showed a lot of hubris when they faced the tyranid threat, and Satys suffered for it, so the symbol for their failure is the "Falling Eagle."
This (unfinished) version of it is simplified from my original sketch but shows the basics of the icon's look. If you're not quite sure what you're looking at, it's an eagle falling. At the bottom, you see the top of his head looking up past his belly, toward his tail. At the top of the banner pole, incidentally, you might notice the wings are also upside down, further mirroring the falling eagle concept.
The red field symbolizes the tyranid invasion from the skies, while the green is that of the Aurora Chapter, which saved Satys from its own pride.
Variations of the banner will have different iterations of parchments and banners with the chapter (bad latin) slogan: "Hubris, Damnum -- Humilitas, Victorias."
Choosing the Falling Eagle as my icon has also helped me decide what kind of army the Orphans will field: A drop pod army, of course! Satys's Orphans aka The Falling Eagles (perhaps Falling Eagles could be the name of the elites, such as my terminators.)
I'm not versed in WH40K rules (the last game I played was in 1994,) so I haven't the slightest idea of what army composition a Satys force will have. I'll first figure out a tactical style and go from there. I'm sure the ideas will come as I develop my chapter some more.
Until then, "Hubris, Damnum -- Humilitas, Victorias!"
By the way, here's a flag I painted a few years ago. It's a full-size (rough) copy of the Bedford Flag, the first known flag of the American Revolution, carried by Nathaniel Page at the Battle of Concord: