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    "### 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"
   ]
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    "application \"fan\";"
   ]
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    "\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"
   ]
  },
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   "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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    "\n",
    "\n",
    "Since some of the input polytopes may be redundant, you should ask for the `MAXIMAL_POLYTOPES`.\n",
    "\n",
    "    \n"
   ]
  },
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       "{0 1 2}\n",
       "{2 3}\n",
       "\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print $pc1->MAXIMAL_POLYTOPES;"
   ]
  },
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    "\n",
    "{{ :tutorial:pcom2.png }}\n",
    "\n",
    "#### Triangulations\n",
    "\n",
    "Triangulations of polytopes form an important special class of polytopal complexes.  In polymake they are objects of type `SimplicialComplex` (and thus belong to the application `topaz`).  However, it is easy to convert them as follows:\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$c=cube(3);\n",
    "$triangulation=new PolyhedralComplex(VERTICES=>$c->VERTICES,MAXIMAL_POLYTOPES=>$c->TRIANGULATION->FACETS);"
   ]
  },
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    "\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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