# Polygon prefixes

Polygons are named after the number of sides that they have. A pentagon has 5 sides, an octagon has 8 sides. But how are they named? What's the name for a 248-sided polygon?

All polygons are suffixed with -gon. There are specific prefixes for each polygon depending on the number of sides. Here are the prefixes for the lower numbers:

3 - tri
4 - tetra
5 - penta
6 - hexa
7 - hepta
8 - octa
9 - nona
10 - deca
11 - undeca
12 - dodeca
13 - triskaideca
20 - icosa


Polygons with 21 to 99 sides have a different system. Take the prefix for the tens digit (found on the left column), the ones digit (right column below), and then stick a "kai" between them to get (tens)kai(ones)gon.

10 - deca        | 1 - hena
20 - icosi       | 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 - nonaconta   | 9 - nona


The 3-digit sided polygons are named in a similar fashion. A 100-sided polygon is called a hectogon. Take the hundreds digit, find it on the column for ones digits, then stick a "hecta" to its right. Now number off the tens and ones like above: (hundreds)hecta(tens)kai(ones)gon. If the hundreds place digit is a 1, don't put the prefix behind "hecta"; if the ones place is 0, then omit the (ones) section.

So, given an integer (3 <= n <= 999), return the name of an n-sided polygon. n-gon is not a valid answer :P

As with all code golf, shortest code wins.

• 100-sided is hectogon or hectagon? The tens digit above 100 is also unclear. I guess 110 and 120 are hectahenakaigon and hectadikaigon (or hectaicosikaigon?) Feb 17, 2013 at 10:29
• Also, 101-sided is "hectakaihenagon" (as I understand from your rules) or "hectahenagon"? Feb 17, 2013 at 11:39
• @beary605 I think nona- is wrong. That would be from latin and the others, hepta-, hexa- are from greek. It should be ennea-. I know the wikipedia says nonagon is OK!
– user7467
Feb 17, 2013 at 20:41
• @felipa: I was debating whether to have it be ennea-, but I've heard "nonagon" more often than "enneagon", so I went with that. Feb 17, 2013 at 21:49
• @ugoren: 100 - hectagon, and I didn't see that I didn't have deca, thanks for pointing that out. 110 - hectadecagon, 120 - hectaicosigon. 101 - hectakaihenagon. Feb 17, 2013 at 21:52

## C, 401, 391

Lets put something out there so there is at least one answer for reference :-)

char*s[]={"","hena","di","tri","tetra","penta","hexa","hepta","octa","nona","un","do","triskai","deca","icosi","tria","conta","kai","icosa","hecto","hecta","gon\n"};
p(i){printf(s[i]);}
t;n(i){
if(i<10)
p(i);   // ones
else if(i<20){
i-=10;
p(i+(i&&i<4)*9); // teens
p(13); // "deca"
}else if(i==20)
p(18); // "icosa"
else if(i==100)
p(19); // "hecto"
else{
t=i/100;
p(t>1?t:0); // hundreds
p(t?20:0);  // "hecta"
i%=100;
t=i/10;
p(t+(t&&t<4)*12); // tens
p(t>2?16:0);      // "conta"
i%=10;
p(i?17:0); // "kai"
p(i);      // ones
}
p(21); // "gon\n"
}


Test with:

main(){
for(int i=3;i<=999;i++){
printf("%3d: ",i);n(i);
}
}


Subset of output:

  3: trigon
4: tetragon
5: pentagon
6: hexagon
7: heptagon
8: octagon
9: nonagon
10: decagon
11: undecagon
12: dodecagon
13: triskaidecagon
20: icosagon
21: icosikaihenagon
22: icosikaidigon
23: icosikaitrigon
...
99: nonacontakainonagon
100: hectogon
101: hectakaihenagon
102: hectakaidigon
103: hectakaitrigon
104: hectakaitetragon
105: hectakaipentagon
106: hectakaihexagon
107: hectakaiheptagon
108: hectakaioctagon
109: hectakainonagon
...
997: nonahectanonacontakaiheptagon
998: nonahectanonacontakaioctagon
999: nonahectanonacontakainonagon

• Nice. You can replace if..else with ?: (and ; with ,) to save some characters. Also t>1&&p(t) and similar changes can help. And I'm not sure, but perhaps you could rearrange s so that the constants you use would be single digit. Feb 20, 2013 at 9:12

## JavaScript - 405 386

Version 1: (405 chars)

i=prompt(),o='0hena0di0tri0tetra0penta0hexa0hepta0octa0nona'.split(0),d='0W0icosi0triaQ0tetraQ0pentaQ0hexaQ0heptaQ0octaQ0nonaQ'.split(0),t='W0unW0doW0triskaiW0tetraW0pentaW0hexaW0heptaW0octaW0nonaW0icosa'.split(0),x=('000'+i).substr(-3).split('');alert((i<10?o[i]:i<21?t[i-10]:i==100?'hecto':(i<100?'':i<200?'hecta':o[x]+'hecta')+d[x]+'kai'+o[x]).replace(/Q/g,'conta').replace(/W/g,'deca')+'gon')


Version 2: (386 chars)

i=prompt(),p='0tetra0penta0hexa0hepta0octa0nona',o='0hena0di0tri'+p,t=('W0unW0doW0triskai'+p.replace(/0/g,'W0')+'W0icosa').split(0),x=('000'+i).substr(-3).split(''),o=o.split(0);alert((i<10?o[i]:i<21?t[i-10]:i==100?'hecto':(i<100?'':i<200?'hecta':o[x]+'hecta')+('0W0icosi0tria'+p.replace(/0/g,'Q0')+'Q').split(0)[x]+'kai'+o[x]).replace(/Q/g,'conta').replace(/W/g,'deca')+'gon')


Output example:

3: trigon
4: tetragon
5: pentagon
6: hexagon
7: heptagon
8: octagon
9: nonagon
10: decagon
11: undecagon
12: dodecagon
13: triskaidecagon
20: icosagon
21: icosikaihenagon
22: icosikaidigon
23: icosikaitrigon
99: nonacontakainonagon
...
100: hectogon
101: hectakaihenagon
102: hectakaidigon
103: hectakaitrigon
104: hectakaitetragon
105: hectakaipentagon
106: hectakaihexagon
107: hectakaiheptagon
108: hectakaioctagon
109: hectakainonagon
...
997: nonahectanonacontakaiheptagon
998: nonahectanonacontakaioctagon
999: nonahectanonacontakainonagon


# Cobra - 370 bytes

This is currently a function, but if that isn't allowed then I'll change it.

def f(x) as String
o='. hena di tri tetra penta hexa hepta octa nona'.split
o,t,h,d='',['','deca','icosci','triconta'],['','hecta','dihecta','trihecta'],['undeca','dodeca','triskaideca']
for z in 4:10,t,h,d=t+[o[z]+'conta'],h+[o[z]+'hecta'],d+[o[z]+'deca']
for z in 10,t[z]+='kai'
return if(x-100,h[x//100]+if(10<x<20,d[x-11],t[x%100//10]+o[x%10]),'hecto')+'gon'


And for some reason the cobra highlighter has // set as a comment, which is wrong.