In geometry, a polygon /ˈpɒlɪɡɒn/ 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 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
editPolygons are always named by prefixes from Greek numbers.
English cardinal number | English ordinal number | Greek cardinal number | Greek ordinal number |
---|---|---|---|
one | first | hena | protos |
two | second | dyo | deuteros |
three | third | tria | tritos |
four | fourth | tessera | tetartos |
five | fifth | pente | pemptos |
six | sixth | hexi | 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 | dekatria | dekatos tritos |
fourteen | fourteenth | dekatessera | dekatos tetartos |
fifteen | fifteenth | dekapente | dekatos pemptos |
sixteen | sixteenth | dekahexi | dekatos hektos |
seventeen | seventeenth | dekahepta | dekatos hebdomos |
eighteen | eighteenth | dekaokto | dekatos ogdoös |
nineteen | nineteenth | dekaennea | dekatos enatos |
twenty | twentieth | eikosi | eikostos |
twenty one | twentieth first | eikosi hena | eikostos protos |
twenty two | twentieth second | eikosi dyo | eikostos deuteros |
twenty three | twentieth third | eikosi tria | eikostos tritos |
twenty four | twentieth fourth | eikosi tessera | eikostos tetartos |
twenty five | twentieth fifth | eikosi pente | eikostos pemptos |
twenty six | twentieth sixth | eikosi hexi | eikostos hektos |
twenty seven | twentieth seventh | eikosi hepta | eikostos hebdomos |
twenty eight | twentieth eighth | eikosi okto | eikostos ogdoös |
twenty nine | twentieth ninth | eikosi ennea | eikostos enatos |
thirty | thirtieth | trianta | triakostos |
thirty one | thirtieth first | trianta hena | triakostos protos |
thirty two | thirtieth second | trianta dyo | triakostos deuteros |
forty | fortieth | saranta | tessarakostos |
fifty | fiftieth | penenta | pentekostos |
sixty | sixtieth | hexenta | hexekostos |
seventy | seventieth | hebdomenta | hebdomekostos |
eighty | eightieth | ogdonta | ogdoëkostos |
ninety | ninetieth | enenenta | enenekostos |
hundred | hundredth | hekato | hekatostos |
hundred ten | hundredth tenth | hekaton deka | hekatostos dekatos |
hundred twenty | hundredth twentieth | hekaton eikosi | hekatostos eikostos |
two hundred | two hundredth | diakosia | diakosiostos |
three hundred | three hundredth | triakosia | triakosiostos |
four hundred | four hundredth | tetrakosia | tetrakosiostos |
five hundred | five hundredth | pentakosia | pentakosiostos |
six hundred | six hundredth | hexakosia | hexakosiostos |
seven hundred | seven hundredth | heptakosia | heptakosiostos |
eight hundred | eight hundredth | oktakosia | oktakosiostos |
nine hundred | nine hundredth | enneakosia | enneakosiostos |
thousand | thousandth | chilia | chiliostos |
two thousand | second thousandth | dyo chiliades | deuteros chiliostos |
three thousand | third thousandth | tria chiliades | tritos chiliostos |
four thousand | fourth thousandth | tessera chiliades | tetartos chiliostos |
five thousand | fifth thousandth | pente chiliades | pemptos chiliostos |
six thousand | sixth thousandth | hexi chiliades | hektos chiliostos |
seven thousand | seventh thousandth | hepta chiliades | hebdomos chiliostos |
eight thousand | eighth thousandth | okto chiliades | ogdoös chiliostos |
nine thousand | ninth thousandth | ennea chiliades | enatos chiliostos |
ten thousand | tenth thousandth | deka chiliades | dekatos chiliostos |
twenty thousand | twentieth thousandth | eikosi chiliades | eikostos chiliostos |
thirty thousand | thirtieth thousandth | trianta chiliades | triakostos chiliostos |
forty thousand | fortieth thousandth | saranta chiliades | tessarakostos chiliostos |
fifty thousand | fiftieth thousandth | penenta chiliades | pentekostos chiliostos |
sixty thousand | sixtieth thousandth | hexenta chiliades | hexekostos chiliostos |
seventy thousand | seventieth thousandth | hebdomenta chiliades | hebdomekostos chiliostos |
eighty thousand | eightieth thousandth | ogdonta chiliades | ogdoëkostos chiliostos |
ninety thousand | ninetieth thousandth | enenenta chiliades | enenekostos chiliostos |
hundred thousand | hundredth thousandth | hekato chiliades | hekatostos chiliostos |
two hundred thousand | two hundredth thousandth | diakosia chiliades | diakosiostos chiliostos |
three hundred thousand | three hundredth thousandth | triakosia chiliades | triakosiostos chiliostos |
million | millionth | chilia chiliades | chiliostos chiliostos |
Systematic polygon names
editTo construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows.
Tens | Ones | final suffix | ||
---|---|---|---|---|
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]
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 | trideca- | 23 | icosi-tri- | 33 | triaconta-tri- | 400 | tetrahecta- |
4 | tetra- | 14 | tetradeca- | 24 | icosi-tetra- | 40 | tetraconta- | 500 | pentahecta- |
5 | penta- | 15 | pentadeca- | 25 | icosi-penta- | 50 | pentaconta- | 600 | hexahecta- |
6 | hexa- | 16 | hexadeca- | 26 | icosi-hexa- | 60 | hexaconta- | 700 | heptahecta- |
7 | hepta- | 17 | heptadeca- | 27 | icosi-hepta- | 70 | heptaconta- | 800 | octahecta- |
8 | octa- | 18 | octadeca- | 28 | icosi-octa- | 80 | octaconta- | 900 | enneahecta- |
9 | ennea- | 19 | enneadeca- | 29 | icosi-ennea- | 90 | enneaconta- |
List of n-gons by Greek numerical prefixes
editSides | Names | |||
---|---|---|---|---|
1 | henagon | monogon | ||
2 | digon | |||
3 | trigon | triangle | ||
4 | tetragon | quadrilateral | ||
5 | pentagon | |||
6 | hexagon | |||
7 | heptagon | |||
8 | octagon | |||
9 | enneagon | nonagon | ||
10 | decagon | |||
11 | hendecagon | |||
12 | dodecagon | |||
13 | tridecagon | |||
14 | tetradecagon | |||
15 | pentadecagon | |||
16 | hexadecagon | |||
17 | heptadecagon | |||
18 | octadecagon | |||
19 | enneadecagon | |||
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 | diacosiagon | ||
300 | trihectagon | triacosiagon | ||
400 | tetrahectagon | tetracosiagon | ||
500 | pentahectagon | pentacosiagon | ||
600 | hexahectagon | hexacosiagon | ||
700 | heptahectagon | heptacosiagon | ||
800 | octahectagon | octacosiagon | ||
900 | enneahectagon | enneacosiagon | ||
1000 | chiliagon | |||
2000 | dichiliagon | |||
3000 | trichiliagon | |||
4000 | tetrachiliagon | |||
5000 | pentachiliagon | |||
6000 | hexachiliagon | |||
7000 | heptachiliagon | |||
8000 | octachiliagon | |||
9000 | enneachiliagon | |||
10000 | decachiliagon | myriagon | ||
20000 | icosachiliagon | |||
30000 | triacontachiliagon | |||
40000 | tetracontachiliagon | |||
50000 | pentacontachiliagon | |||
60000 | hexacontachiliagon | |||
70000 | heptacontachiliagon | |||
80000 | octacontachiliagon | |||
90000 | enneacontachiliagon | |||
100000 | hecatochiliagon | |||
200000 | diacosiachiliagon | |||
300000 | triacosiachiliagon | |||
1000000 | hecatommyriagon | megagon | ||
∞ | apeirogon |
See also
editReferences
edit- ^ "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.
- NAMING POLYGONS
- Benjamin Franklin Finkel, A Mathematical Solution Book Containing Systematic Solutions to Many of the Most Difficult Problems, 1888