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Usually, solid shapes have more than two faces; if that is the case, then the simplest shape we are looking at is a triangular pyramid (both upright and oblique pyramids are considered here).

However, if you're looking for a two-faced solid, then you'll be fresh out of luck, even with non-Euclidean geometry, as you cannot have an equilateral triangle and an isosceles triangle in the same shape (unless you make the isosceles triangle an equilateral one).

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