- #1

GreyArea

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Johnson Solid J2 is a pentagonal pyramid consisting of five equilateral triangles on a pentagonal pase, meeting at the apex. It's the shape you get if you slice off the top five triangular faces of an icosahedron.

I can find a lot of info on this shape, height, surface area etc, but I need to know one specific angle that eludes me; the angle formed by the junction of;

1. A vertical line dropped from the apex of the solid to the base

2. a line that bisects one of the equilateral triangles, rising from the mid point of base of the triangle to its apex

If it can be calculated as a function of the height of the pyramid, or the height of the face that's fine, but I get the feeling it SHOULD be a constant value, similar to the dihedral angle of (approx) 138 .2 degrees that is formed by the junction of any pair of triangular faces in this solid.

Thanks for your help!