Key dimensions

Hi.

I'm having a hard time modelling a simple piano keyboard. I looked online for dimensions (probably haven't tried hard enough) but I figured it shouldn't be too time consuming.

Turns out I was wrong.

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Here, the white keys were laid out first. The black keys were subsequently placed in the middle between two white keys

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In this model, the width of a white keys back part and the width of a black key is identical. The front parts of the white keys all have equal width

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Could anyone explain what's going on here? There's this big ugly gap in the second screenshot which is obviously not there in a real piano. How are the real keys dimensioned?