I did find this tidbit on
Alfred L. Kennedy that made a reference to the college.
"In 1842 he had established the Philadelphia school of chemistry, and remained at its head until 1853, when it became under a new charter the Polytechnic college of the state of Pennsylvania. He was then chosen its president."
There are some other references to Polytechnic College of the State of Pennsylvania, so perhaps this might be the correct - or formal - name of the college.
For what it is worth, Upsilon was charted in 1865 and I believe closed around/by 1900. I'm not sure if the chapter closed before, or due to, the closure/absorbing of the college.