Page 1 of 1

### Perles Irrational Polytope (in polymake)

Posted: 11 Mar 2020, 20:07
Hello,

I have the following naive question.

The vertices of perles 8-dimensional irrational polytope are expressed in terms of the square root of 5, denoted r5.

For example one coordinate of one vertex is " -1/2 + 1/2r5".

I am not fully certain whether this expression is -1/2 + (1/2)r5 or -1/2 + 1/(2r5) , although I suspect the latter.

Thanks

### Re: Perles Irrational Polytope (in polymake)

Posted: 11 Mar 2020, 21:18
I am not fully certain whether this expression is -1/2 + (1/2)r5 or -1/2 + 1/(2r5) , although I suspect the latter.
No, the former. The quadratic extension numbers are always normalized, having square roots in the numerator.

### Re: Perles Irrational Polytope (in polymake)

Posted: 11 Mar 2020, 22:15
I see, thanks.

Also, is it possible to compute the convex hull of irrational vectors (say with coordinates in a quadratic extension), and then compute the facets of the resulting polytope?

### Re: Perles Irrational Polytope (in polymake)

Posted: 11 Mar 2020, 22:20
Yes, it's possible: