tetraeder with one dimension

Hi,

I'm having a problem to make, in wildfire, a tetraeder. I can't make the
model with one dimension.



I want for modification reasons one dimension variable. So I can easy blow
up the model.



Who can help me?

Laurens





For definition of a tetraeder see
http://www.hhg-muenchen.de/homepage/mundn/geo10a/3pyramid/tetra/defini.htm)

 

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


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

 

: Hi,
:
: I'm having a problem to make, in wildfire, a tetraeder. I can't make the
: model with one dimension.
: I want for modification reasons one dimension variable. So I can easy blow
: up the model.
: Who can help me?
:
: Laurens
: For definition of a tetraeder see
: http://www.hhg-muenchen.de/homepage/mundn/geo10a/3pyramid/tetra/defini.htm)
:
:
I used the Wolfram site for data on the tetrahedron. Especially the dihedral
angle. Though the number they give is adequate, it is rounded up. The more closely
you can calculate the dihedral, the closer you'll come to a true Platonic solid.
http://mathworld.wolfram.com/Tetrahedron.html

The method, in summary, that I used in Pro/e was to create a blend of an isoceles
triangle, built on a construction circle (dimensioned as reference) for the first
section, and a point for the second section. I gave an arbitrary distance between
the sections (the height of the pyramid), then modified this with a relation. The
relation set the section distance to the radius of the construction circle times
the tangent of the dihedral angle, taken as 70.53 degrees.

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

 

:
: > The method, in summary, that I used in Pro/e was to create a blend of an
: isoceles
: > triangle, built on a construction circle (dimensioned as reference) for
: the first
: > section, and a point for the second section. I gave an arbitrary distance
: between
: > the sections (the height of the pyramid), then modified this with a
: relation. The
: > relation set the section distance to the radius of the construction circle
: times
: > the tangent of the dihedral angle, taken as 70.53 degrees.
: >
: > 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

 

: Good site David. The cubic construction knocks spots off mine, and is
exact.

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.