• To: mathgroup at smc.vnet.net
• Subject: [mg104798] Re: [mg104765] A Question about Combinatorica
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Tue, 10 Nov 2009 06:00:10 -0500 (EST)

```pts = {{0., 0., 1.},
{0.181636, 0.559017, 0.809017},
{-0.769421, 0.559017, 0.309017},
{-0.769421, -0.559017, -0.309017},
{0.181636, -0.559017, -0.809017}};

p1 = Permutations[pts];

Length[p1] == 5!

True

Guessing what you mean by similarities:

pts2 = Union[pts,
SameTest -> (Abs[#1] == Abs[#2] &)]

{{-0.769421, -0.559017, -0.309017}, {0., 0., 1.},
{0.181636, -0.559017, -0.809017}}

p2 = Permutations[pts2];

Length[p2] == 3!

True

Bob Hanlon

---- Marwa Abd El-Wahaab <m.a.elwahaab at gmail.com> wrote:

=============
Dear Sir

I have a question about  permutations of 5 points in 3D space .

These 5 points are on the surface of a sphere of radius =1.

These points are:
{ {0., 0., 1.},  {0.181636, 0.559017, 0.809017},  {-0.769421,
0.559017, 0.309017}, {-0.769421, -0.559017, -0.309017}, {0.181636,
-0.559017, -0.809017} }

My question:

What are all possible permutations for these 5 points ?

What are the permutations after delete similarities?

Thanks

Marwa Ali

```

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