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Does this equilateral triangle represent the base of an equilateral pyramid inside of a corresponding sphere?

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Does this equilateral triangle represent the base of an equilateral pyramid inside of a corresponding sphere?

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Here is what I found, glory be to G-d: The objective was to find out if this equilateral triangle is also representative of an equilateral pyramid inside of a corresponding sphere. The triangle has 2 sides and the measurement of each side of the outer square is 2 9/16 thus revealing that the circle has a pole/diameter of the same measurement, (2 9/16) see Fig. D below. I will also use some of the original drawings which were measured by hand, on paper, to help validate this article.

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