See apeirogon on Wiktionary
{
"derived": [
{
"_dis1": "0 0",
"word": "apeirogonal"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "apeiro",
"3": "gon"
},
"expansion": "apeiro- + -gon",
"name": "confix"
}
],
"etymology_text": "From apeiro- + -gon.",
"forms": [
{
"form": "apeirogons",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "apeirogon (plural apeirogons)",
"name": "en-noun"
}
],
"hyphenation": [
"apei‧ro‧gon"
],
"hyponyms": [
{
"_dis1": "0 0",
"english": "a specific non-regular case",
"word": "zerogon"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"_dis1": "0 0",
"word": "apeirohedron"
},
{
"_dis1": "0 0",
"word": "infinigon"
},
{
"_dis1": "0 0",
"word": "pseudogon"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "47 53",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "48 52",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "48 52",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "46 54",
"kind": "other",
"langcode": "en",
"name": "Non-Euclidean geometry",
"orig": "en:Non-Euclidean geometry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "48 52",
"kind": "topical",
"langcode": "en",
"name": "Polygons",
"orig": "en:Polygons",
"parents": [
"Shapes",
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247:",
"text": "Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.",
"type": "quote"
},
{
"ref": "1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27:",
"text": "In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.",
"type": "quote"
},
{
"ref": "2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, →ISBN, page 217:",
"text": "[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.",
"type": "quote"
},
{
"ref": "2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:",
"text": "There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.",
"type": "quote"
}
],
"glosses": [
"A type of generalised polygon with a countably infinite number of sides and vertices;"
],
"id": "en-apeirogon-en-noun-kmYVzbm6",
"links": [
[
"mathematics",
"mathematics"
],
[
"geometry",
"geometry"
],
[
"polygon",
"polygon"
],
[
"countably infinite",
"countably infinite"
],
[
"side",
"side"
],
[
"vertices",
"vertex"
],
[
"limit case",
"limit case"
],
[
"regular polygon",
"regular polygon"
],
[
"infinity",
"infinity"
],
[
"edge",
"edge"
],
[
"straight line",
"straight line"
],
[
"partition",
"partition"
],
[
"point",
"point"
]
],
"raw_glosses": [
"(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "47 53",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "42 58",
"kind": "other",
"name": "English terms prefixed with apeiro-",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "44 56",
"kind": "other",
"name": "English terms suffixed with -gon",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "29 71",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "48 52",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "48 52",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "42 58",
"kind": "other",
"name": "Terms with Bulgarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "37 63",
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "36 64",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "42 58",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "41 59",
"kind": "other",
"name": "Terms with Macedonian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "37 63",
"kind": "other",
"name": "Terms with Polish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "35 65",
"kind": "other",
"name": "Terms with Russian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "40 60",
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "other",
"langcode": "en",
"name": "Infinity",
"orig": "en:Infinity",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "46 54",
"kind": "other",
"langcode": "en",
"name": "Non-Euclidean geometry",
"orig": "en:Non-Euclidean geometry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "43 57",
"kind": "other",
"langcode": "en",
"name": "Shapes in non-Euclidean geometry",
"orig": "en:Shapes in non-Euclidean geometry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "48 52",
"kind": "topical",
"langcode": "en",
"name": "Polygons",
"orig": "en:Polygons",
"parents": [
"Shapes",
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
}
],
"glosses": [
"A type of generalised polygon with a countably infinite number of sides and vertices;\n(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.",
"the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points."
],
"id": "en-apeirogon-en-noun-qu37Bae5",
"links": [
[
"mathematics",
"mathematics"
],
[
"geometry",
"geometry"
],
[
"polygon",
"polygon"
],
[
"countably infinite",
"countably infinite"
],
[
"side",
"side"
],
[
"vertices",
"vertex"
],
[
"limit case",
"limit case"
],
[
"regular polygon",
"regular polygon"
],
[
"infinity",
"infinity"
],
[
"edge",
"edge"
],
[
"straight line",
"straight line"
],
[
"partition",
"partition"
],
[
"point",
"point"
]
],
"raw_glosses": [
"(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;"
],
"raw_tags": [
"in the regular case"
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "39 61",
"code": "bg",
"lang": "Bulgarian",
"roman": "bezkrajnoǎgǎlnik",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "безкрайноъгълник"
},
{
"_dis1": "39 61",
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "ääretönkulmio"
},
{
"_dis1": "39 61",
"code": "fr",
"lang": "French",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "apeirogone"
},
{
"_dis1": "39 61",
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"neuter"
],
"word": "Unendlicheck"
},
{
"_dis1": "39 61",
"code": "mk",
"lang": "Macedonian",
"roman": "beskonečnoagolnik",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "бесконечноаголник"
},
{
"_dis1": "39 61",
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "wielokąt z nieskończoną liczbą katów"
},
{
"_dis1": "39 61",
"code": "ru",
"lang": "Russian",
"roman": "apejrogón",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "апейрого́н"
},
{
"_dis1": "39 61",
"code": "ru",
"lang": "Russian",
"roman": "beskonečnougólʹnik",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "бесконечноуго́льник"
},
{
"_dis1": "39 61",
"code": "es",
"lang": "Spanish",
"sense": "Translations",
"word": "apeirógono"
}
]
}
],
"sounds": [
{
"ipa": "/əˈpiːɹɵɡɑn/"
},
{
"ipa": "/əˈpeɪ̯ɹɵɡɑn/"
},
{
"audio": "LL-Q1860 (eng)-Vealhurl-apeirogon.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.ogg"
}
],
"word": "apeirogon"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English nouns",
"English terms prefixed with apeiro-",
"English terms suffixed with -gon",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Bulgarian translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Macedonian translations",
"Terms with Polish translations",
"Terms with Russian translations",
"Terms with Spanish translations",
"Translation table header lacks gloss",
"en:Infinity",
"en:Non-Euclidean geometry",
"en:Polygons",
"en:Shapes in non-Euclidean geometry"
],
"derived": [
{
"word": "apeirogonal"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "apeiro",
"3": "gon"
},
"expansion": "apeiro- + -gon",
"name": "confix"
}
],
"etymology_text": "From apeiro- + -gon.",
"forms": [
{
"form": "apeirogons",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "apeirogon (plural apeirogons)",
"name": "en-noun"
}
],
"hyphenation": [
"apei‧ro‧gon"
],
"hyponyms": [
{
"english": "a specific non-regular case",
"word": "zerogon"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "apeirohedron"
},
{
"word": "infinigon"
},
{
"word": "pseudogon"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Geometry",
"en:Mathematics"
],
"examples": [
{
"ref": "1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247:",
"text": "Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.",
"type": "quote"
},
{
"ref": "1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27:",
"text": "In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.",
"type": "quote"
},
{
"ref": "2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, →ISBN, page 217:",
"text": "[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.",
"type": "quote"
},
{
"ref": "2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:",
"text": "There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.",
"type": "quote"
}
],
"glosses": [
"A type of generalised polygon with a countably infinite number of sides and vertices;"
],
"links": [
[
"mathematics",
"mathematics"
],
[
"geometry",
"geometry"
],
[
"polygon",
"polygon"
],
[
"countably infinite",
"countably infinite"
],
[
"side",
"side"
],
[
"vertices",
"vertex"
],
[
"limit case",
"limit case"
],
[
"regular polygon",
"regular polygon"
],
[
"infinity",
"infinity"
],
[
"edge",
"edge"
],
[
"straight line",
"straight line"
],
[
"partition",
"partition"
],
[
"point",
"point"
]
],
"raw_glosses": [
"(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"en:Geometry",
"en:Mathematics"
],
"glosses": [
"A type of generalised polygon with a countably infinite number of sides and vertices;\n(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.",
"the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"geometry",
"geometry"
],
[
"polygon",
"polygon"
],
[
"countably infinite",
"countably infinite"
],
[
"side",
"side"
],
[
"vertices",
"vertex"
],
[
"limit case",
"limit case"
],
[
"regular polygon",
"regular polygon"
],
[
"infinity",
"infinity"
],
[
"edge",
"edge"
],
[
"straight line",
"straight line"
],
[
"partition",
"partition"
],
[
"point",
"point"
]
],
"raw_glosses": [
"(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;"
],
"raw_tags": [
"in the regular case"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/əˈpiːɹɵɡɑn/"
},
{
"ipa": "/əˈpeɪ̯ɹɵɡɑn/"
},
{
"audio": "LL-Q1860 (eng)-Vealhurl-apeirogon.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav/LL-Q1860_%28eng%29-Vealhurl-apeirogon.wav.ogg"
}
],
"translations": [
{
"code": "bg",
"lang": "Bulgarian",
"roman": "bezkrajnoǎgǎlnik",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "безкрайноъгълник"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "ääretönkulmio"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "apeirogone"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"neuter"
],
"word": "Unendlicheck"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "beskonečnoagolnik",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "бесконечноаголник"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "wielokąt z nieskończoną liczbą katów"
},
{
"code": "ru",
"lang": "Russian",
"roman": "apejrogón",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "апейрого́н"
},
{
"code": "ru",
"lang": "Russian",
"roman": "beskonečnougólʹnik",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "бесконечноуго́льник"
},
{
"code": "es",
"lang": "Spanish",
"sense": "Translations",
"word": "apeirógono"
}
],
"word": "apeirogon"
}
Download raw JSONL data for apeirogon meaning in All languages combined (7.1kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.