/usr/share/polymake/demo/pcom.ipynb is in polymake-common 3.2r2-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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"cells": [
{
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"source": [
"### Polyhedral complexes in polymake\n",
"\n",
"Polyhedral complexes are contained in the application `fan`, so you hanve to switch application to access the full functionality.\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"application \"fan\";"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"To define polyhedral complexes in `polymake`, you need to provide an array of input points and a list of polytopes represented as an array of arrays of point indices.\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"$pc1 = new PolyhedralComplex(POINTS=>[[1,0,0],[1,0,1],[1,1,0],[1,1,1]],INPUT_POLYTOPES=>[[0,1,2],[2,3],[1]]);"
]
},
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"source": [
"\n",
"\n",
"Since some of the input polytopes may be redundant, you should ask for the `MAXIMAL_POLYTOPES`.\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{0 1 2}\n",
"{2 3}\n",
"\n"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"print $pc1->MAXIMAL_POLYTOPES;"
]
},
{
"attachments": {},
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"source": [
"\n",
"{{ :tutorial:pcom2.png }}\n",
"\n",
"#### Triangulations\n",
"\n",
"Triangulations of polytopes form an important special class of polytopal complexes. In polymake they are objects of type `SimplicialComplex` (and thus belong to the application `topaz`). However, it is easy to convert them as follows:\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"$c=cube(3);\n",
"$triangulation=new PolyhedralComplex(VERTICES=>$c->VERTICES,MAXIMAL_POLYTOPES=>$c->TRIANGULATION->FACETS);"
]
},
{
"attachments": {},
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"source": [
"\n",
"#### Voronoi Diagrams and regular subdivisions\n",
"\n",
"There are seperate tutorials for [Voronoi diagrams](voronoi) and [regluar subdivisions](regular_subdivisions) of point sets.\n"
]
}
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