Mathematical Pyry

Looking at the 2 lovely pictures of our beloved pyramid I began musing on the mathematics of her radiance...
(I hope I am right and would appreciate any corrections to mein mistakes)
1. The pyry was a square based pyramid.
2. Each face was an equilateral triangle, rather than an isocelese or scalene one.
3. Therefore each edge of the 3 triangular faces was the same length(unknown) and the 3 angles of each face was 60 degrees (the total being 180 degrees)
4. It had 5 vertices, 5 faces and 8 edges...

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