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List of polygons
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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.
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 cardinal number | English ordinal number | Greek cardinal number | Greek ordinal number |
---|---|---|---|
one | first | heis (fem. mia, neut. hen) | protos |
two | second | duo | deuteros |
three | third | treis | tritos |
four | fourth | tettares | tetartos |
five | fifth | pente | pemptos |
six | sixth | hex | hektos |
seven | seventh | hepta | hebdomos |
eight | eighth | okto | ogdoös |
nine | ninth | ennea | enatos |
ten | tenth | deka | dekatos |
eleven | eleventh | hendeka | hendekatos |
twelve | twelfth | dodeka | dodekatos |
thirteen | thirteenth | triskaideka | dekatotritos |
fourteen | fourteenth | tettareskaideka | dekatotetartos |
fifteen | fifteenth | pentekaideka | dekatopemptos |
sixteen | sixteenth | hekkaideka | dekatohektos |
seventeen | seventeenth | heptakaideka | dekatohebdomos |
eighteen | eighteenth | oktokaideka | dekatoögdoös |
nineteen | nineteenth | enneakaideka | dekatoënatos |
twenty | twentieth | eikosi | eikostos |
twenty-one | twenty-first | heiskaieikosi | eikostoprotos |
twenty-two | twenty-second | duokaieikosi | eikostodeuteros |
twenty-three | twenty-third | triskaieikosi | eikostotritos |
twenty-four | twenty-fourth | tetterakaieikosi | eikostotetartos |
twenty-five | twenty-fifth | pentekaieikosi | eikostopemptos |
twenty-six | twenty-sixth | hekkaieikosi | eikostohektos |
twenty-seven | twenty-seventh | heptakaieikosi | eikostohebdomos |
twenty-eight | twenty-eighth | oktokaieikosi | eikostoögdoös |
twenty-nine | twenty-ninth | enneakaieikosi | eikostoënatos |
thirty | thirtieth | triakonta | triakostos |
thirty-one | thirty-first | heiskaitriakonta | triakostoprotos |
forty | fortieth | tessarakonta | tessarakostos |
fifty | fiftieth | pentekonta | pentekostos |
sixty | sixtieth | hexekonta | hexekostos |
seventy | seventieth | hebdomekonta | hebdomekostos |
eighty | eightieth | ogdoëkonta | ogdoëkostos |
ninety | ninetieth | enenekonta | enenekostos |
hundred | hundredth | hekaton | hekatostos |
hundred and ten | hundred and tenth | dekakaihekaton | hekatostodekatos |
hundred and twenty | hundred and twentieth | ikosikaihekaton | hekatostoikostos |
two hundred | two hundredth | diakosioi | diakosiostos |
three hundred | three hundredth | triakosioi | triakosiostos |
four hundred | four hundredth | tetrakosioi | tetrakosiostos |
five hundred | five hundredth | pentakosioi | pentakosiostos |
six hundred | six hundredth | hexakosioi | hexakosiostos |
seven hundred | seven hundredth | heptakosioi | heptakosiostos |
eight hundred | eight hundredth | oktakosioi | oktakosiostos |
nine hundred | nine hundredth | enneakosioi | enneakosiostos |
thousand | thousandth | chilioi | chiliostos |
two thousand | two thousandth | dischilioi | dischiliostos |
three thousand | three thousandth | trischilioi | trischiliostos |
four thousand | four thousandth | tetrakischilioi | tetrakischiliostos |
five thousand | five thousandth | pentakischilioi | pentakischiliostos |
six thousand | six thousandth | hexakischilioi | hexakischiliostos |
seven thousand | seven thousandth | heptakischilioi | heptakischiliostos |
eight thousand | eight thousandth | oktakischilioi | oktakischiliostos |
nine thousand | nine thousandth | enneakischilioi | enneakischiliostos |
ten thousand | ten thousandth | myrioi | myriastos |
twenty thousand | twenty thousandth | dismyrioi | dismyriastos |
thirty thousand | thirty thousandth | trismyrioi | trismyriastos |
forty thousand | forty thousandth | tetrakismyrioi | tetrakismyriastos |
fifty thousand | fifty thousandth | pentakismyrioi | pentakismyriastos |
sixty thousand | sixty thousandth | hexakismyrioi | hexakismyriastos |
seventy thousand | seventy thousandth | heptakismyrioi | heptakismyriastos |
eighty thousand | eighty thousandth | oktakismyrioi | oktakismyriastos |
ninety thousand | ninety thousandth | enneakismyrioi | enneakismyriastos |
hundred thousand | hundred thousandth | dekakismyrioi | dekakismyriastos |
two hundred thousand | two hundred thousandth | ikosakismyrioi | ikosakismyriastos |
three hundred thousand | three hundred thousandth | triakontakismyrioi | triakontakismyriastos |
million | millionth | hekatontakismyrioi | hekatontakismyriastos |
two million | two millionth | diakosakismyrioi | diakosakismyriastos |
three million | three millionth | triakosakismyrioi | triakosakismyriastos |
ten million | ten millionth | chiliakismyrioi | chiliakismyriastos |
hundred million | hundred millionth | myriakismyrioi | myriakismyriastos |
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 | ||
20 | icosi- (icosa- when alone) | 2 | -di- | ||
30 | triaconta- | 3 | -tri- | ||
40 | tetraconta- | 4 | -tetra- | ||
50 | pentaconta- | 5 | -penta- | ||
60 | hexaconta- | 6 | -hexa- | ||
70 | heptaconta- | 7 | -hepta- | ||
80 | octaconta- | 8 | -octa- | ||
90 | enneaconta- | 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.[citation needed]
Ones | Tens | Twenties | Thirties+ | Hundreds | |||||
---|---|---|---|---|---|---|---|---|---|
10 | deca- | 20 | icosa- | 30 | triaconta- | 100 | hecta- | ||
1 | hena- | 11 | hendeca- | 21 | icosi-hena- | 31 | triaconta-hena- | 200 | dihecta- |
2 | di- | 12 | dodeca- | 22 | icosi-di- | 32 | triaconta-di- | 300 | trihecta- |
3 | tri- | 13 | triskaideca- | 23 | icosi-tri- | 33 | triaconta-tri- | 400 | tetrahecta- |
4 | tetra- | 14 | tetrakaideca- | 24 | icosi-tetra- | 40 | tetraconta- | 500 | pentahecta- |
5 | penta- | 15 | pentakaideca- | 25 | icosi-penta- | 50 | pentaconta- | 600 | hexahecta- |
6 | hexa- | 16 | hexakaideca- | 26 | icosi-hexa- | 60 | hexaconta- | 700 | heptahecta- |
7 | hepta- | 17 | heptakaideca- | 27 | icosi-hepta- | 70 | heptaconta- | 800 | octahecta- |
8 | octa- | 18 | octakaideca- | 28 | icosi-octa- | 80 | octaconta- | 900 | enneahecta- |
9 | ennea- | 19 | enneakaideca- | 29 | icosi-ennea- | 90 | enneaconta- |
List of n-gons by Greek numerical prefixes[]
Sides | Names | |||
---|---|---|---|---|
1 | henagon | monogon | ||
2 | digon | bigon | ||
3 | trigon | triangle | ||
4 | tetragon | quadrilateral | ||
5 | pentagon | |||
6 | hexagon | |||
7 | heptagon | septagon | ||
8 | octagon | |||
9 | enneagon | nonagon | ||
10 | decagon | |||
11 | hendecagon | undecagon | ||
12 | dodecagon | |||
13 | tridecagon | triskaidecagon | ||
14 | tetradecagon | tetrakaidecagon | ||
15 | pentadecagon | pentakaidecagon | ||
16 | hexadecagon | hexakaidecagon | ||
17 | heptadecagon | heptakaidecagon | ||
18 | octadecagon | octakaidecagon | ||
19 | enneadecagon | enneakaidecagon | ||
20 | icosagon | |||
21 | icosikaihenagon | icosihenagon | ||
22 | icosikaidigon | icosidigon | icosadigon | |
23 | icosikaitrigon | icositrigon | icosatrigon | |
24 | icosikaitetragon | icositetragon | icosatetragon | |
25 | icosikaipentagon | icosipentagon | icosapentagon | |
26 | icosikaihexagon | icosihexagon | icosahexagon | |
27 | icosikaiheptagon | icosiheptagon | icosaheptagon | |
28 | icosikaioctagon | icosioctagon | icosaoctagon | |
29 | icosikaienneagon | icosienneagon | icosaenneagon | |
30 | triacontagon | |||
31 | triacontakaihenagon | triacontahenagon | tricontahenagon | |
32 | triacontakaidigon | triacontadigon | tricontadigon | |
33 | triacontakaitrigon | triacontatrigon | tricontatrigon | |
34 | triacontakaitetragon | triacontatetragon | tricontatetragon | |
35 | triacontakaipentagon | triacontapentagon | tricontapentagon | |
36 | triacontakaihexagon | triacontahexagon | tricontahexagon | |
37 | ||||
38 | triacontakaioctagon | tricontaoctagon | ||
39 | triacontakaienneagon | tricontaenneagon | ||
40 | tetracontagon | tessaracontagon | ||
41 | tetracontakaihenagon | tessaracontahenagon | ||
42 | tetracontakaidigon | tetracontadigon | tessaracontadigon | |
43 | tetracontakaitrigon | tetracontatrigon | tessaracontatrigon | |
44 | tetracontakaitetragon | tessaracontatetragon | ||
45 | tetracontakaipentagon | tetracontapentagon | tessaracontapentagon | |
46 | tetracontakaihexagon | tessaracontahexagon | ||
47 | tetracontakaiheptagon | tessaracontaheptagon | ||
48 | tetracontakaioctagon | tetracontaoctagon | tessaracontaoctagon | |
49 | tetracontakaienneagon | tessaracontaenneagon | ||
50 | pentacontagon | pentecontagon | ||
51 | pentacontakaihenagon | pentacontahenagon | pentecontahenagon | |
52 | pentacontakaidigon | pentacontadigon | pentecontadigon | |
53 | pentacontakaitrigon | pentacontatrigon | pentecontatrigon | |
54 | pentacontakaitetragon | pentacontatetragon | pentecontatetragon | |
55 | pentacontakaipentagon | pentacontapentagon | pentecontapentagon | |
56 | pentacontakaihexagon | pentacontahexagon | pentecontahexagon | |
57 | pentacontakaiheptagon | pentacontaheptagon | pentecontaheptagon | |
58 | pentacontakaioctagon | pentacontaoctagon | pentecontaoctagon | |
59 | pentacontakaienneagon | pentacontaenneagon | pentecontaenneagon | |
60 | hexacontagon | hexecontagon | ||
61 | hexacontakaihenagon | hexacontahenagon | hexecontahenagon | |
62 | hexacontakaidigon | hexacontadigon | hexecontadigon | |
63 | hexacontakaitrigon | hexacontatrigon | hexecontatrigon | |
64 | hexacontakaitetragon | hexacontatetragon | hexecontatetragon | |
65 | hexacontakaipentagon | hexacontapentagon | hexecontapentagon | |
66 | hexacontakaihexagon | hexacontahexagon | hexecontahexagon | |
67 | hexacontakaiheptagon | hexacontaheptagon | hexecontaheptagon | |
68 | hexacontakaioctagon | hexacontaoctagon | hexecontaoctagon | |
69 | hexacontakaienneagon | hexacontaenneagon | hexecontaenneagon | |
70 | heptacontagon | hebdomecontagon | ||
71 | heptacontakaihenagon | heptacontahenagon | hebdomecontahenagon | |
72 | heptacontakaidigon | heptacontadigon | hebdomecontadigon | |
73 | heptacontakaitrigon | heptacontatrigon | hebdomecontatrigon | |
74 | heptacontakaitetragon | heptacontatetragon | hebdomecontatetragon | |
75 | heptacontakaipentagon | heptacontapentagon | hebdomecontapentagon | |
76 | heptacontakaihexagon | heptacontahexagon | hebdomecontahexagon | |
77 | heptacontakaiheptagon | heptacontaheptagon | hebdomecontaheptagon | |
78 | heptacontakaioctagon | heptacontaoctagon | hebdomecontaoctagon | |
79 | heptacontakaienneagon | heptacontaenneagon | hebdomecontaenneagon | |
80 | octacontagon | ogdoecontagon | ||
81 | octacontakaihenagon | octacontahenagon | ogdoecontahenagon | |
82 | octacontakaidigon | octacontadigon | ogdoecontadigon | |
83 | octacontakaitrigon | octacontatrigon | ogdoecontatrigon | |
84 | octacontakaitetragon | octacontatetragon | ogdoecontatetragon | |
85 | octacontakaipentagon | octacontapentagon | ogdoecontapentagon | |
86 | octacontakaihexagon | octacontahexagon | ogdoecontahexagon | |
87 | octacontakaiheptagon | octacontaheptagon | ogdoecontaheptagon | |
88 | octacontakaioctagon | octacontaoctagon | ogdoecontaoctagon | |
89 | octacontakaienneagon | octacontaenneagon | ogdoecontaenneagon | |
90 | enneacontagon | enenecontagon | ||
91 | enneacontakaihenagon | enneacontahenagon | enenecontahenagon | |
92 | enneacontakaidigon | enneacontadigon | enenecontadigon | |
93 | enneacontakaitrigon | enneacontatrigon | enenecontatrigon | |
94 | enneacontakaitetragon | enneacontatetragon | enenecontatetragon | |
95 | enneacontakaipentagon | enneacontapentagon | enenecontapentagon | |
96 | enneacontakaihexagon | enneacontahexagon | enenecontahexagon | |
97 | enneacontakaiheptagon | enneacontaheptagon | enenecontaheptagon | |
98 | enneacontakaioctagon | enneacontaoctagon | enenecontaoctagon | |
99 | enneacontakaienneagon | enneacontaenneagon | enenecontaenneagon | |
100 | hectogon | hecatontagon | hecatogon | |
120 | hecatonicosagon | dodecacontagon | ||
200 | dihectagon | diacosigon | ||
300 | trihectagon | triacosigon | ||
400 | tetrahectagon | tetracosigon | ||
500 | pentahectagon | pentacosigon | ||
600 | hexahectagon | hexacosigon | ||
700 | heptahectagon | heptacosigon | ||
800 | octahectagon | octacosigon | ||
900 | enneahectagon | enacosigon | ||
1000 | chiliagon | |||
2000 | dischiliagon | dichiliagon | ||
3000 | trischiliagon | trichiliagon | ||
4000 | tetrakischiliagon | tetrachiliagon | ||
5000 | pentakischiliagon | pentachiliagon | ||
6000 | hexakischiliagon | hexachiliagon | ||
7000 | heptakischiliagon | heptachiliagon | ||
8000 | octakischiliagon | octachiliagon | ||
9000 | enneakischiliagon | enneachilliagon | ||
10000 | myriagon | |||
20000 | dismyriagon | dimyriagon | ||
30000 | trismyriagon | trimyriagon | ||
40000 | tetrakismyriagon | tetramyriagon | ||
50000 | pentakismyriagon | pentamyriagon | ||
60000 | hexakismyriagon | hexamyriagon | ||
70000 | heptakismyriagon | heptamyriagon | ||
80000 | octakismyriagon | octamyriagon | ||
90000 | enneakismyriagon | enneamyriagon | ||
100000 | decakismyriagon | decamyriagon | ||
200000 | icosakismyriagon | icosamyriagon | ||
300000 | triacontakismyriagon | tricontamyriagon | ||
400000 | tetracontakismyriagon | tetracontamyriagon | ||
500000 | pentacontakismyriagon | pentacontamyriagon | ||
600000 | hexacontakismyriagon | hexacontamyriagon | ||
700000 | heptacontakismyriagon | heptacontamyriagon | ||
800000 | octacontakismyriagon | octacontamyriagon | ||
900000 | enneacontakismyriagon | enneacontamyriagon | ||
1000000 | hecatontakismyriagon | megagon | ||
2000000 | diacosakismyriagon | dimegagon | ||
3000000 | triacosakismyriagon | trimegagon | ||
4000000 | tetracosakismyriagon | tetramegagon | ||
5000000 | pentacosakismyriagon | pentamegagon | ||
6000000 | hexacosakismyriagon | hexamegagon | ||
7000000 | heptacosakismyriagon | heptamegagon | ||
8000000 | octacosakismyriagon | octamegagon | ||
9000000 | enneacosakismyriagon | enneamegagon | ||
10000000 | chiliakismyriagon | decamegagon | ||
20000000 | dischiliakismyriagon | icosamegagon | ||
30000000 | trischiliakismyriagon | tricontamegagon | ||
40000000 | tetrakischiliakismyriagon | tetracontamegagon | ||
50000000 | pentakischiliakismyriagon | pentacontamegagon | ||
60000000 | hexakischiliakismyriagon | hexacontamegagon | ||
70000000 | heptakischiliakismyriagon | heptacontamegagon | ||
80000000 | octakischiliakismyriagon | octacontamegagon | ||
90000000 | enneakischiliakismyriagon | enneacontamegagon | ||
100000000 | myriakismyriagon | hectamegagon | ||
1 000 000 000 | gigagon | |||
1 000 000 000 000 | teragon | |||
∞ | apeirogon |
See also[]
References[]
- ^ "Greek and Latin words for numbers". AWE. Hull University.
- ^ 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.
- ^ "Naming Polygons and Polyhedra". The Math Forum. Drexel University.
- ^ "Naming Polygons". The Math Forum. Drexel University.
- ^ Most listed names for hundreds do not follow actual Greek number system.
- NAMING POLYGONS
- Benjamin Franklin Finkel, A Mathematical Solution Book Containing Systematic Solutions to Many of the Most Difficult Problems, 1888
- Polygons
- Mathematics-related lists