"4-polytope" meaning in All languages combined

{
  "etymology_text": "From 4-dimensional + polytope.",
  "forms": [
    {
      "form": "4-polytopes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "4-polytope (plural 4-polytopes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
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            "Entries with incorrect language header",
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        },
        {
          "kind": "other",
          "name": "Terms with Italian translations",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Higher-dimensional geometry",
          "orig": "en:Higher-dimensional geometry",
          "parents": [
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
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        }
      ],
      "examples": [
        {
          "ref": "1984, London Mathematical Society lecture note series, numbers 88-90, page 101:",
          "text": "Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.",
          "type": "quote"
        },
        {
          "ref": "2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:",
          "text": "The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.",
          "type": "quote"
        },
        {
          "ref": "2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes, page 40:",
          "text": "For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].",
          "type": "quote"
        }
      ],
      "glosses": [
        "A four-dimensional polytope."
      ],
      "id": "en-4-polytope-en-noun-FesFp0NZ",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "four-dimensional",
          "four-dimensional"
        ],
        [
          "polytope",
          "polytope"
        ]
      ],
      "raw_glosses": [
        "(geometry) A four-dimensional polytope."
      ],
      "synonyms": [
        {
          "sense": "4-dimensional polytope",
          "word": "polycell"
        },
        {
          "sense": "4-dimensional polytope",
          "word": "polychoron"
        },
        {
          "sense": "4-dimensional polytope",
          "word": "polyhedroid"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "it",
          "lang": "Italian",
          "sense": "4-dimensional polytope",
          "tags": [
            "masculine"
          ],
          "word": "policoro"
        }
      ],
      "wikipedia": [
        "4-polytope"
      ]
    }
  ],
  "word": "4-polytope"
}

{
  "etymology_text": "From 4-dimensional + polytope.",
  "forms": [
    {
      "form": "4-polytopes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "4-polytope (plural 4-polytopes)",
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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    {
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        "Terms with Italian translations",
        "en:Geometry",
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      "examples": [
        {
          "ref": "1984, London Mathematical Society lecture note series, numbers 88-90, page 101:",
          "text": "Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.",
          "type": "quote"
        },
        {
          "ref": "2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:",
          "text": "The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.",
          "type": "quote"
        },
        {
          "ref": "2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes, page 40:",
          "text": "For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].",
          "type": "quote"
        }
      ],
      "glosses": [
        "A four-dimensional polytope."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "four-dimensional",
          "four-dimensional"
        ],
        [
          "polytope",
          "polytope"
        ]
      ],
      "raw_glosses": [
        "(geometry) A four-dimensional polytope."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "4-polytope"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "4-dimensional polytope",
      "word": "polycell"
    },
    {
      "sense": "4-dimensional polytope",
      "word": "polychoron"
    },
    {
      "sense": "4-dimensional polytope",
      "word": "polyhedroid"
    }
  ],
  "translations": [
    {
      "code": "it",
      "lang": "Italian",
      "sense": "4-dimensional polytope",
      "tags": [
        "masculine"
      ],
      "word": "policoro"
    }
  ],
  "word": "4-polytope"
}