The document you cited was a patent application, not a granted patent. The subsequent patent is US9414970B2. It is important to look at an actual patent instead of it's application because the claims in a patent are often narrower than the corresponding application. Patent coverage is defined by its claims. Reading the bulk of a patent can sometimes give the impression that it broadly covers a technology where the actual claim language might be fairly narrow. Here is the first claim:
A method of noninvasively reducing facial wrinkles formed in facial skin, comprising the steps of
providing a skin patch comprising a
membrane and having a skin contacting surface, the skin contacting
surface comprising a film of silicone-containing material to which an
additive has been added to said silicone-containing material prior to
cross-linking of the silicone-containing material, said
silicone-containing material having the additive impregnated therein
and after cross-linking of the silicone-containing material to said
membrane,
wherein said additive is a therapeutic active ingredient,
wherein said skin patch skin contacting surface comprises a
cross-linked composition of said silicone-containing material and said
therapeutic active ingredient on said membrane, said
silicone-containing material being cross-linked to said membrane,
applying the skin contacting surface of the skin patch over and into
contact with facial wrinkles, and
maintaining the skin patch in place
over and in contact with the facial wrinkles for an effective amount
of time to tighten the skin at and around the facial wrinkles, thereby
reducing the facial wrinkles in said skin, by contacting the skin with
said skin patch silicone material film and delivering a treatment of
said active ingredient contained in said patch to said skin by
contacting the skin with the already cross-linked together surface of
silicone-containing material and membrane containing said active
ingredient to deliver said active ingredient from said film;
the
additive being useful for wrinkle reduction and/or other clinical
indications; and
the additive being peptides, vitamin compounds,
antioxidants, growth factors, glycolic or alphahydroxy acids, or
combinations thereof.
As you can see, this claim is fairly long and involved. In order to infringe on a patent, you need to infringe on at least one claim. To infringe on a claim, you need to implement each and every aspect of the claim. Thus if a claim details steps A, B, C and D and you only implement steps A, B and D, you don't infringe. This claim has a lot of steps in it. For instance it specifies a silicone containing material with a "therapeutic active ingredient". If you use a non-silicone adhesive you are free from this claim. Similarly the additive must be one or more of the following: "peptides, vitamin compounds, antioxidants, growth factors, glycolic or alphahydroxy acids".
A similar analysis must be done with each of the claims in the patent. Note that a claim that refers to another claim is a dependent claim and is only infringed if the cited claim is also infringed. Thus it is usually best to focus on the independent claims first.
To try to address your specific questions:
If I cut a piece of medical tape to a similar shape (a triangle),
could this be considered an infringement of this patent?
In other words, can the combination of a simple shape with an existing material ever be considered a patent infringement?
I don't believe so since the medical tape wouldn't incorporate a therapeutic active ingredient.
Is the purpose (keeping the skin in place) part of the
invention/patent? Is there a difference in a piece of tape for your
face vs a piece of tape for industrial use, in the context of deciding
whether patent infringement occurred?
Again, the patent's coverage is defined by its claims. Every independent claim refers to skin, in particular facial skin. If you have a product using tape for something other than reducing wrinkles in skin, I suspect it is clear of this patent.
Please be advised that I am not a lawyer and this isn't legal advice. I always recommend consulting with an actual patent attorney when determining freedom to operate.