List of polygons
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/01/Regular_polygon_5_annotated.svg/220px-Regular_polygon_5_annotated.svg.png)
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- | ||||
1 | hena- | 11 | hendeca- | 21 | icosi-hena- | 31 | triaconta-hena- | 100 | hecta- |
2 | di- | 12 | dodeca- | 22 | icosi-di- | 32 | triaconta-di- | 200 | dihecta- |
3 | tri- | 13 | triskaideca- | 23 | icosi-tri- | 33 | triaconta-tri- | 300 | trihecta- |
4 | tetra- | 14 | tetrakaideca- | 24 | icosi-tetra- | 40 | tetraconta- | 400 | tetrahecta- |
5 | penta- | 15 | pentakaideca- | 25 | icosi-penta- | 50 | pentaconta- | 500 | pentahecta- |
6 | hexa- | 16 | hexakaideca- | 26 | icosi-hexa- | 60 | hexaconta- | 600 | hexahecta- |
7 | hepta- | 17 | heptakaideca- | 27 | icosi-hepta- | 70 | heptaconta- | 700 | heptahecta- |
8 | octa- | 18 | octakaideca- | 28 | icosi-octa- | 80 | octaconta- | 800 | octahecta- |
9 | ennea- | 19 | enneakaideca- | 29 | icosi-ennea- | 90 | enneaconta- | 900 | enneahecta- |
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 | triacontakaiheptagon | triacontaheptagon | tricontaheptagon | |
38 | triacontakaioctagon | triacontaoctagon | tricontaoctagon | |
39 | triacontakaienneagon | triacontaenneagon | tricontaenneagon | |
40 | tetracontagon | tessaracontagon | ||
41 | tetracontakaihenagon | tetracontahenagon | tessaracontahenagon | |
42 | tetracontakaidigon | tetracontadigon | tessaracontadigon | |
43 | tetracontakaitrigon | tetracontatrigon | tessaracontatrigon | |
44 | tetracontakaitetragon | tetracontatetragon | tessaracontatetragon | |
45 | tetracontakaipentagon | tetracontapentagon | tessaracontapentagon | |
46 | tetracontakaihexagon | tetracontahexagon | tessaracontahexagon | |
47 | tetracontakaiheptagon | tetracontaheptagon | tessaracontaheptagon | |
48 | tetracontakaioctagon | tetracontaoctagon | tessaracontaoctagon | |
49 | tetracontakaienneagon | tetracontaenneagon | 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 | triacontamegagon | ||
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 | |||
1 000 000 000 000 000 | petagon | |||
1 000 000 000 000 000 000 | exagon | |||
1 000 000 000 000 000 000 000 | zettagon | |||
1 000 000 000 000 000 000 000 000 | yottagon | |||
1 000 000 000 000 000 000 000 000 000 | xennagon | |||
1 000 000 000 000 000 000 000 000 000 000 | dakagon | |||
10^33 | hendakagon | |||
10^36 | dokagon | |||
10^39 | tedakagon | |||
10^42 | tetradakagon | |||
10^45 | pedakagon | |||
10^48 | hedakagon | |||
10^51 | zedakagon | |||
10^54 | yodakagon | |||
10^57 | nedakagon | |||
10^60 | ikagon | |||
10^90 | trakagon | |||
10^100 | googolgon | |||
10^120 | ||||
’’’tekagon’’’ | ∞ | 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