Set Equal edge length

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Set Equal edge length

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I'm trying to marry equilateral triangles against the sides of a cubic plane.

ALL edges SHOULD be the same length if the base of the triangle, the length
of it's two sides and the cubic plane are all set to the same length.

The problem is, I'm not exactly sure how to go about that.

What would be the easiest way to do that?

I'm trying to test a theory of symmetrical pattern involving building out (and on) equilateral triangles against cubic planes and vice versa.  Something, I guess, maybe comparable to penrose tilings?

It requires that all edges be the same length.

I don't think bisecting a cubic plane is the same thing?  Is it?

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