tetraeder with one dimension

Make a sphere, then 2 cuts aligned to it will do the job.

You need an angle too, but that isn't variable

With a single leg of the base dimensioned and driving the size, it is possible to change this to any number and have the tetrahedron update correctly.

David Janes

Good site David. The cubic construction knocks spots off mine, and is exact. The inradius/outradius ratio of 3:1 is pretty good for construction from just one dimension when all relationships are expressed in geometry

: > With a single leg of the base dimensioned and driving the size, it is : possible to : > change this to any number and have the tetrahedron update correctly. : >

: > David Janes : : Good site David. The cubic construction knocks spots off mine, and is exact. : The inradius/outradius ratio of 3:1 is pretty good for construction from : just one dimension when all relationships are expressed in geometry : Actually, I thought you must at least have had the geometry coordinates for each of the four vertices. Since they would have been points on a sphere, I figured you used them to constuct cuves and planes which would have been needed for making your two cuts. The Wolfram data does give those points as well as some angles from the centroid.

So much to it, no wonder Pythagoras got lost in it. Wasn't it the tetrahedron that drove him crazy?

David Janes

Dunno. After a generous slug of Van Winkle bourbon last night it took me about an hour to derive the stuff on the Wolfram site & I still didn't have time for 'the cube' and it was certainly doing my head no good.

I used to be good at this stuff until someone gave me a machine to do it for me.