tetrahedron in a sphere question

[padren]

I am doing this 3D app that has some annoying trig in it, that is kind of messing with my head, as I am not the best trig guy on the planet...so please help!

 

I start with 4 equilateral triangles, to make a tetrahedron, and all I want is to really have each point in the triangle touch a radius of a sphere.

 

I map everything in horiz/vert degrees, to get the base down...

 

I start with the "top down" and draw out on graph paper, an equilateral triangle and put a dot in the center, and draw a circle around it. I make isosceles triangles by drawing lines from the dots to the points, so you have three of those inside it, and it looks like the center point out of each triangle is 120 degrees, and the corners are 30 degrees each.

 

Since I want "triangle one" to face zero degrees, I map the first two points as -60 and 60, or 300 and 60 to avoid negatives in a 360 degree space.

 

The second triangle's horizontal values are 60 to 180, and the last 180 to 300.

 

I think I have the base values all correct.

 

Now, for the vertical aspect, I have I want the tip of the tetrahedron to point straight up, which is 90 degrees vertical from the plane, so I figure, based on the same info, I should have it go down to -30, so that would be 120 degrees total using those inner isosceles triangles as reference points.

 

Therefore, I think I should be able to use degree coordinates of points at 300,330 60,330 and 0,90 to plot "triangle one" and just step the "x" by 120 degrees and leave the "y" values the same to make the other two "up pointing" sides, and then plot the bottom 4th triangle as 300,330 60,330 and 180,330 to what I want.

 

 

What I need to know - are those presumptions correct for the base values?

 

I have a formula that seems to work perfectly where all I have to do is supply a radius and it should use the degree values to make my tetrahedron, but it looks "stretched" and not quite right. I am not sure if my starting values are messed up, or the formula has some weird bug in it.

 

I am posting in math and not compsci because this really seems to be a math issue, I can code alright, but the math makes my brain melt in 3D.

 

If it would help, I can post my formula to take degree coords and return a x,y,z coord based on a fixed radius, but I really want to know if my base radial coordinates are correct or not.

 

TIA!