Custom QPushButton shape

I'm trying to create a very simple pentagonal custom button in Qt. I'm using PyQt5, but the concepts and style-sheet code should be the same as C++ anyway.

My current code is this:

Code:

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button = QPushButton()
button.setFixedSize(QSize(20, 15))
button.setSizePolicy(QSizePolicy(QSizePolicy.Fixed, QSizePolicy.Fixed))
x = button.width()
y = button.height()
points = [QPoint(0, 0), QPoint(x/2, 0), QPoint(x, y/2), QPoint(x/2, y), QPoint(0, y)]
button.setMask(QRegion(QPolygon(points)))

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This almost works great, but unfortunately it ruins the dropshadow effect and the button just ends up looking weird: https://i.stack.imgur.com/tXsgF.png

Removing the border with

Code:

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button.setStyleSheet("border-style: none")

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doesn't work well because then the button is indistinguishable from the background. What I'm currently using is

Code:

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button.setStyleSheet("background-color: darkBlue; border-style: none")

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but this makes the button blue (which is not ideal) and it also removes the colour changes when hovering or clicking the button. Ideally, I would like to have

Code:

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button.setStyleSheet("border-style: outset")

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and keep colour changing functionality you'd expect from a button. However, the above line actually does the same as `border-style: none`, simply removing the border. Is there a way to get an outset border or at least fix the dropshadow effect of the original button?