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14 Jun 2024, 10:16
Forum: General Discussion
Topic: Maximal number of (in)equalities allowed for polytope.
Replies: 2
Views: 220

### Re: Maximal number of (in)equalities allowed for polytope.

It is not easy or next to impossible to predict the amount of resources required for a convex hull computation a priori. There is only McMullen's upper bound theorem, which gives some guidance. For instance, this is the maximal number of facets of a polytope in dimension 10 with 10! vertices. polyto...
13 Jun 2024, 12:32
Forum: Helpdesk
Topic: Stanley-Reisner ideal of polytope
Replies: 1
Views: 187

### Re: Stanley-Reisner ideal of polytope

Your approach only works in the smooth case. In that case the toric variety (defined by the normal fan of the polytope) is simplicial. Intersecting the normal fan gives a finite simplicial complex, and its non-faces give you the Stanley-Reisner ring. See polymake's topaz documentation . See also OSC...
29 May 2024, 13:37
Forum: Helpdesk
Topic: Confused by error message from truncation
Replies: 1
Views: 726

### Re: Confused by error message from truncation

Your code complies with what is allowed in the docs. So it's probably a bug. Stay tuned.
29 May 2024, 11:54
Forum: General Discussion
Topic: Plotting Binary Icosahedral
Replies: 3
Views: 1016

### Re: Plotting Binary Icosahedral

The group SL(2, 5) does not have a faithful 3-dimensional real representation. Thus it does not act as a group of symmetries of a 3-dimensional object such as an icosahedron.
But then, what exactly do you expect polymake to do for you?
28 May 2024, 10:03
Forum: General Discussion
Topic: Plotting Binary Icosahedral
Replies: 3
Views: 1016

### Re: Plotting Binary Icosahedral

I have no idea what the "binary icosahedron" should be; and so there is no standard polymake function for this. Please explain.

As far as saving files from a visualization is concerned, please consult our tutorial.
08 May 2024, 09:47
Forum: Helpdesk
Topic: union of cones
Replies: 1
Views: 561

### Re: union of cones

Here is a simple example (not mathematically interesting):

Code: Select all

polytope > @list_of_cones = (); for (my $i=0;$i<5; ++$i) { my$C = new Cone(INPUT_RAYS=>[[1,0],[1,$i]]); push @list_of_cones,$C; } polytope > $u = fan::union_of_cones(\@list_of_cones); polytope > print$u->F_VECTOR; 5 4
15 Apr 2024, 09:54
Forum: General Discussion
Topic: Plotting Icosahedron in Polymake
Replies: 2
Views: 2290

### Re: Plotting Icosahedron in Polymake

To show the regular icosahedron you can just use icosahedron()->VISUAL; or icosahedron()->VISUAL_GRAPH; if you only want to see the vertices and the edges. What you will get exactly will depend on the configuration of your setup, the default backend being threejs. To show the four planes additionall...
03 Apr 2024, 11:35
Forum: Helpdesk
Topic: "ERROR: Cannot draw zero cycle at ... "
Replies: 4
Views: 5209

### Re: "ERROR: Cannot draw zero cycle at ... "

Sorry, the correct homogenization of your example is the following. $quadric = toTropicalPolynomial("max(2*x,1+x+y,2+2*y,1+y+z,2*z,4+2*w)");$TQuadric = new Hypersurface<Max>(POLYNOMIAL=>$quadric);$TQuadric->VISUAL; My previous explanation is valid: the input needs to be homogeneous, i.e....
24 Mar 2024, 12:15
Forum: Helpdesk
Topic: "ERROR: Cannot draw zero cycle at ... "
Replies: 4
Views: 5209

### Re: "ERROR: Cannot draw zero cycle at ... "

polymake uses homogeneous polynomials throughout. Please replace the first line of your code by

Code: Select all

$quadric = toTropicalPolynomial("max(2*x,w+x+y,2*w+2*y,w+y+z,2*z,4*w)"); See this tutorial and these jupyter notebooks for more examples. 18 Oct 2023, 15:53 Forum: Helpdesk Topic: Recognizing the topology of surfaces Replies: 8 Views: 16833 ### Re: Recognizing the topology of surfaces Could you please upload your $my_dual_sub and $my_signs? One way would be to save the $S_0 object and share the resulting JSON.

I can't promise, but maybe we can do a bit more here.

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