Greg Neill wrote:
> "Spaceman" <space...@yourclockmalfunctioned.duh> wrote in message
> news:RNqdnUP-EoLM-gnVnZ2dnUVZ_g-dnZ2d@comcast.com
>> john_m_stan...@yahoo.co.uk wrote:
>>> A friend and I are having a bet. He states that there must be
>>> objects or mechanisms with 8 degrees of freedom
>>> (not counting translation} which
>>> have 3-fold symmetry (at least in some
>>> configurations). But we cannot find any.

>>> He is thinking of objects like a deformable cubus with corners
>>> whose angles are not fixed. But such a cubus has
>>> - three orientational degrees of freedom
>>> - three internal angles
>>> which makes a total of only 6 degrees of freedom.
>>> A cubus has 3fold symmetry when seen along
>>> a diagonal, so that would fit; but 6 are not 8
>>> degrees of freedom.

>>> I brought up the idea of a tetrahedral skeleton,
>>> (like a methane molecule http://en.wikipedia.org/wiki/Methane ) .
>>> It has 8 degrees of freedom,
>>> it has 3fold symmetry in some configurations,
>>> but we do not see a way to build that in metal
>>> or rubber without having more or less than 8 degrees
>>> of freedom.

>>> On the other hand, I am not able to prove
>>> that the puzzle is impossible to solve.

>>> Is there another solution? Where can one look for such
>>> objects or related theorems? Are there books or sites
>>> on these issues?

>>> Thanks in advance!

>> Hi John,
>> The shape or makeup of an object does not change the freedom
>> of it's motion.
>> Freedom of motion has 6 directions, up- down, forward-
>> backward,left-right. Those are the 6 "so called degrees" that I would
>> call planes of motion instead.
>> 6 maximum planes of motion only.

> In his first paragraph John specifically discounted
> translational degrees of freedom.  Another swing and
> a miss for James.