There are only 8 possible angles that you should see (ignoring orientation)
In my previous post, we looked at how a fair die has 24 unique orientations — each representing a different way the cube can sit while still being a valid outcome. But there's redundancy baked into those 24 angles.
If we ignore rotation — that is, if we don't care which way the die is twisted around its vertical axis — then all those orientations collapse into just 8 distinct corners.
Here are the de-duped 8 angles:
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1a: 
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1b:
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1c:
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1d:
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6a: 
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6b:
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6c:
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6d:
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I just wanted to make sure I included this de-duplication here for completeness sake. The 24 previously mentioned arrangements all factor in the orientation, but it should be obvious to some people that there can only be 8 corners of the "perfect die".
