List of polygons

In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners.

A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles.

The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον (polygōnon/polugōnon), noun use of neuter of πολύγωνος (polygōnos/polugōnos, the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.

Greek numbers

Polygons are primarily named by prefixes from Ancient Greek numbers.

English-Greek numbers[1][2]
English cardinal numberEnglish ordinal numberGreek cardinal numberGreek ordinal number
onefirstheis (fem. mia, neut. hen)protos
twosecondduodeuteros
threethirdtreistritos
fourfourthtettarestetartos
fivefifthpentepemptos
sixsixthhexhektos
sevenseventhheptahebdomos
eighteighthoktoogdoös
nineninthenneaenatos
tententhdekadekatos
eleveneleventhhendekahendekatos
twelvetwelfthdodekadodekatos
thirteenthirteenthtriskaidekadekatotritos
fourteenfourteenthtettareskaidekadekatotetartos
fifteenfifteenthpentekaidekadekatopemptos
sixteensixteenthhekkaidekadekatohektos
seventeenseventeenthheptakaidekadekatohebdomos
eighteeneighteenthoktokaidekadekatoögdoös
nineteennineteenthenneakaidekadekatoënatos
twentytwentietheikosieikostos
twenty-onetwenty-firstheiskaieikosieikostoprotos
twenty-twotwenty-secondduokaieikosieikostodeuteros
twenty-threetwenty-thirdtriskaieikosieikostotritos
twenty-fourtwenty-fourthtetterakaieikosieikostotetartos
twenty-fivetwenty-fifthpentekaieikosieikostopemptos
twenty-sixtwenty-sixthhekkaieikosieikostohektos
twenty-seventwenty-seventhheptakaieikosieikostohebdomos
twenty-eighttwenty-eighthoktokaieikosieikostoögdoös
twenty-ninetwenty-ninthenneakaieikosieikostoënatos
thirtythirtiethtriakontatriakostos
thirty-onethirty-firstheiskaitriakontatriakostoprotos
fortyfortiethtessarakontatessarakostos
fiftyfiftiethpentekontapentekostos
sixtysixtiethhexekontahexekostos
seventyseventiethhebdomekontahebdomekostos
eightyeightiethogdoëkontaogdoëkostos
ninetyninetiethenenekontaenenekostos
hundredhundredthhekatonhekatostos
hundred and tenhundred and tenthdekakaihekatonhekatostodekatos
hundred and twentyhundred and twentiethikosikaihekatonhekatostoikostos
two hundredtwo hundredthdiakosioidiakosiostos
three hundredthree hundredthtriakosioitriakosiostos
four hundredfour hundredthtetrakosioitetrakosiostos
five hundredfive hundredthpentakosioipentakosiostos
six hundredsix hundredthhexakosioihexakosiostos
seven hundredseven hundredthheptakosioiheptakosiostos
eight hundredeight hundredthoktakosioioktakosiostos
nine hundrednine hundredthenneakosioienneakosiostos
thousandthousandthchilioichiliostos
two thousandtwo thousandthdischilioidischiliostos
three thousandthree thousandthtrischilioitrischiliostos
four thousandfour thousandthtetrakischilioitetrakischiliostos
five thousandfive thousandthpentakischilioipentakischiliostos
six thousandsix thousandthhexakischilioihexakischiliostos
seven thousandseven thousandthheptakischilioiheptakischiliostos
eight thousandeight thousandthoktakischilioioktakischiliostos
nine thousandnine thousandthenneakischilioienneakischiliostos
ten thousandten thousandthmyrioimyriastos
twenty thousandtwenty thousandthdismyrioidismyriastos
thirty thousandthirty thousandthtrismyrioitrismyriastos
forty thousandforty thousandthtetrakismyrioitetrakismyriastos
fifty thousandfifty thousandthpentakismyrioipentakismyriastos
sixty thousandsixty thousandthhexakismyrioihexakismyriastos
seventy thousandseventy thousandthheptakismyrioiheptakismyriastos
eighty thousandeighty thousandthoktakismyrioioktakismyriastos
ninety thousandninety thousandthenneakismyrioienneakismyriastos
hundred thousandhundred thousandthdekakismyrioidekakismyriastos
two hundred thousandtwo hundred thousandthikosakismyrioiikosakismyriastos
three hundred thousandthree hundred thousandthtriakontakismyrioitriakontakismyriastos
millionmillionthhekatontakismyrioihekatontakismyriastos
two milliontwo millionthdiakosakismyrioidiakosakismyriastos
three millionthree millionthtriakosakismyrioitriakosakismyriastos
ten millionten millionthchiliakismyrioichiliakismyriastos
hundred millionhundred millionthmyriakismyrioimyriakismyriastos

Systematic polygon names

To construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows. The "kai" connector is not included by some authors.

Tens and Ones final suffix
-kai- 1 -hena- -gon
20icosi- (icosa- when alone)2-di-
30triaconta-3-tri-
40tetraconta- 4-tetra-
50pentaconta-5-penta-
60hexaconta-6-hexa-
70heptaconta-7-hepta-
80octaconta-8-octa-
90enneaconta-9-ennea-

Extending the system up to 999 is expressed with these prefixes;[3] the names over 99 no longer correspond to how they are actually expressed in Greek.

Polygon names
OnesTensTwentiesThirties+Hundreds
10deca-20icosa-30triaconta-100hecta-
1hena-11hendeca-21icosi-hena-31triaconta-hena-200dihecta-
2di-12dodeca-22icosi-di-32triaconta-di-300trihecta-
3tri-13triskaideca-23icosi-tri-33triaconta-tri-400tetrahecta-
4tetra-14tetrakaideca-24icosi-tetra-40tetraconta-500pentahecta-
5penta-15pentakaideca-25icosi-penta-50pentaconta-600hexahecta-
6hexa-16hexakaideca-26icosi-hexa-60hexaconta-700heptahecta-
7hepta-17heptakaideca-27icosi-hepta-70heptaconta-800octahecta-
8octa-18octakaideca-28icosi-octa-80octaconta-900enneahecta-
9ennea-19enneakaideca-29icosi-ennea-90enneaconta-

List of n-gons by Greek numerical prefixes

List of n-gon names [4][5]
Sides Names
1henagonmonogon
2digonbigon
3trigontriangle
4tetragonquadrilateral
5pentagon
6hexagon
7heptagonseptagon
8octagon
9enneagonnonagon
10decagon
11hendecagonundecagon
12dodecagon
13tridecagontriskaidecagon
14tetradecagontetrakaidecagon
15pentadecagonpentakaidecagon
16hexadecagonhexakaidecagon
17heptadecagonheptakaidecagon
18octadecagonoctakaidecagon
19enneadecagonenneakaidecagon
20icosagon
21icosikaihenagonicosihenagon
22icosikaidigonicosidigonicosadigon
23icosikaitrigonicositrigonicosatrigon
24icosikaitetragonicositetragonicosatetragon
25icosikaipentagonicosipentagonicosapentagon
26icosikaihexagonicosihexagonicosahexagon
27icosikaiheptagonicosiheptagonicosaheptagon
28icosikaioctagonicosioctagonicosaoctagon
29icosikaienneagonicosienneagonicosaenneagon
30triacontagon
31triacontakaihenagontriacontahenagontricontahenagon
32triacontakaidigontriacontadigontricontadigon
33triacontakaitrigontriacontatrigontricontatrigon
34triacontakaitetragontriacontatetragontricontatetragon
35triacontakaipentagontriacontapentagontricontapentagon
36triacontakaihexagontriacontahexagontricontahexagon
37triacontakaiheptagontriacontaheptagontricontaheptagon
38triacontakaioctagontriacontaoctagontricontaoctagon
39triacontakaienneagontriacontaenneagontricontaenneagon
40tetracontagontessaracontagon
41tetracontakaihenagontetracontahenagontessaracontahenagon
42tetracontakaidigontetracontadigontessaracontadigon
43tetracontakaitrigontetracontatrigontessaracontatrigon
44tetracontakaitetragontetracontatetragontessaracontatetragon
45tetracontakaipentagontetracontapentagontessaracontapentagon
46tetracontakaihexagontetracontahexagontessaracontahexagon
47tetracontakaiheptagontetracontaheptagontessaracontaheptagon
48tetracontakaioctagontetracontaoctagontessaracontaoctagon
49tetracontakaienneagontetracontaenneagontessaracontaenneagon
50pentacontagonpentecontagon
51pentacontakaihenagonpentacontahenagonpentecontahenagon
52pentacontakaidigonpentacontadigonpentecontadigon
53pentacontakaitrigonpentacontatrigonpentecontatrigon
54pentacontakaitetragonpentacontatetragonpentecontatetragon
55pentacontakaipentagonpentacontapentagonpentecontapentagon
56pentacontakaihexagonpentacontahexagonpentecontahexagon
57pentacontakaiheptagonpentacontaheptagonpentecontaheptagon
58pentacontakaioctagonpentacontaoctagonpentecontaoctagon
59pentacontakaienneagonpentacontaenneagonpentecontaenneagon
60hexacontagonhexecontagon
61hexacontakaihenagonhexacontahenagonhexecontahenagon
62hexacontakaidigonhexacontadigonhexecontadigon
63hexacontakaitrigonhexacontatrigonhexecontatrigon
64hexacontakaitetragonhexacontatetragonhexecontatetragon
65hexacontakaipentagonhexacontapentagonhexecontapentagon
66hexacontakaihexagonhexacontahexagonhexecontahexagon
67hexacontakaiheptagonhexacontaheptagonhexecontaheptagon
68hexacontakaioctagonhexacontaoctagonhexecontaoctagon
69hexacontakaienneagonhexacontaenneagonhexecontaenneagon
70heptacontagonhebdomecontagon
71heptacontakaihenagonheptacontahenagonhebdomecontahenagon
72heptacontakaidigonheptacontadigonhebdomecontadigon
73heptacontakaitrigonheptacontatrigonhebdomecontatrigon
74heptacontakaitetragonheptacontatetragonhebdomecontatetragon
75heptacontakaipentagonheptacontapentagonhebdomecontapentagon
76heptacontakaihexagonheptacontahexagonhebdomecontahexagon
77heptacontakaiheptagonheptacontaheptagonhebdomecontaheptagon
78heptacontakaioctagonheptacontaoctagonhebdomecontaoctagon
79heptacontakaienneagonheptacontaenneagonhebdomecontaenneagon
80octacontagonogdoecontagon
81octacontakaihenagonoctacontahenagonogdoecontahenagon
82octacontakaidigonoctacontadigonogdoecontadigon
83octacontakaitrigonoctacontatrigonogdoecontatrigon
84octacontakaitetragonoctacontatetragonogdoecontatetragon
85octacontakaipentagonoctacontapentagonogdoecontapentagon
86octacontakaihexagonoctacontahexagonogdoecontahexagon
87octacontakaiheptagonoctacontaheptagonogdoecontaheptagon
88octacontakaioctagonoctacontaoctagonogdoecontaoctagon
89octacontakaienneagonoctacontaenneagonogdoecontaenneagon
90enneacontagonenenecontagon
91enneacontakaihenagonenneacontahenagonenenecontahenagon
92enneacontakaidigonenneacontadigonenenecontadigon
93enneacontakaitrigonenneacontatrigonenenecontatrigon
94enneacontakaitetragonenneacontatetragonenenecontatetragon
95enneacontakaipentagonenneacontapentagonenenecontapentagon
96enneacontakaihexagonenneacontahexagonenenecontahexagon
97enneacontakaiheptagonenneacontaheptagonenenecontaheptagon
98enneacontakaioctagonenneacontaoctagonenenecontaoctagon
99enneacontakaienneagonenneacontaenneagonenenecontaenneagon
100hectogonhecatontagonhecatogon
120hecatonicosagondodecacontagon
200dihectagondiacosigon
300trihectagontriacosigon
400tetrahectagontetracosigon
500pentahectagonpentacosigon
600hexahectagonhexacosigon
700heptahectagonheptacosigon
800octahectagonoctacosigon
900enneahectagonenacosigon
1000chiliagon
2000dischiliagon
3000trischiliagon
4000tetrakischiliagon
5000pentakischiliagon
6000hexakischiliagon
7000heptakischiliagon
8000octakischiliagon
9000enneakischiliagon
10000myriagon
20000dismyriagon
30000trismyriagon
40000tetrakismyriagon
50000pentakismyriagon
60000hexakismyriagon
70000heptakismyriagon
80000octakismyriagon
90000enneakismyriagon
100000decakismyriagon
200000icosakismyriagon
300000triacontakismyriagon
400000tetracontakismyriagon
500000pentacontakismyriagon
600000hexacontakismyriagon
700000heptacontakismyriagon
800000octacontakismyriagon
900000enneacontakismyriagon
1000000hecatontakismyriagonmegagon
2000000diacosakismyriagon
3000000triacosakismyriagon
4000000tetracosakismyriagon
5000000pentacosakismyriagon
6000000hexacosakismyriagon
7000000heptacosakismyriagon
8000000octacosakismyriagon
9000000enneacosakismyriagon
10000000chiliakismyriagon
20000000dischiliakismyriagon
30000000trischiliakismyriagon
40000000tetrakischiliakismyriagon
50000000pentakischiliakismyriagon
60000000hexakischiliakismyriagon
70000000heptakischiliakismyriagon
80000000octakischiliakismyriagon
90000000enneakischiliakismyriagon
100000000myriakismyriagon
apeirogon

See also

References

  1. "Greek and Latin words for numbers". AWE. Hull University.
  2. Lozac'h, N. (1983). "Extension of Rules A-1.1 and A-2.5 Concerning Numerical Terms used in Organic Chemical Nomenclature" (PDF). iupac.org. International Union of Pure and Applied Chemistry.
  3. "Naming Polygons and Polyhedra". The Math Forum. Drexel University.
  4. "Naming Polygons". The Math Forum. Drexel University.
  5. Most listed names for hundreds do not follow actual Greek number system.
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