# Is there a value for $\pi$ that relates to triangles?

So I heard that if one inscribes the largest circle that can fit into a equilateral triangle, then divides the perimeter of the triangle by the diameter of the inscribed circle, it gives a value which can be called "triangle $\pi$", and that value ($\sqrt{27}$) can be used in the place of regular $\pi$ to derive volumes of the other platonic solids. Is that true? Is there a different $\pi$ for triangles? What is that value? Is it close to $\sqrt{27}$? Can it be used to find volumes of platonic solids, especially the icosahedron and the one that looks like a pyramid flipped and stacked on its twin? 4 part question. Thanks we have been arguing about it at work for weeks

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So, what is the question? – Gerry Myerson Jun 14 '12 at 23:48
$\pi$ is a constant, it has only one value... – Alex Becker Jun 15 '12 at 0:03
The word you are looking for is octahedron. – Gerry Myerson Jun 15 '12 at 1:56
If you want to know the volumes of the Platonic solids, try en.wikipedia.org/wiki/…. – Gerry Myerson Jun 15 '12 at 1:59

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