Name That Polygon

By Ana Marie R. Nobleza

W
hat is a hexahectaheptacontakaioctagon? This sounds
unfamiliar, right? But it is actually a polygon. Yes, it is! Greek Prexes
Lets nd out how many sides it has. PREFIX MEANING
Units Digit
hena (or mono) 1
Whats in a Name di 2
When someone asks your name, you denitely answer the word or tri 3
tetra 4
combination of words by which you are called and by means of which penta 5
you can be distinguished or identied. Same goes with everything in hexa 6
the universe. We call them names to identify or distinguish them from hepta 7
octa 8
each other. ennea 9
In math, we always deal with polygons and more often than not, 11 19
hendeca 11
we encounter problems in naming, especially those with more than dodeca 12
10 sides. trideca 13
tetradeca 14
pentadeca 15
Naming Polygons hexadeca 16
WORD BOOSTER Individual polygons are named according heptadeca 17
to the number of sides. Their names are octadeca 18
The word polygon enneadeca 19
comes from the formed by combining a Greek-derived Multiples of 10
late Latin word numerical prex (which tells its number of deca 10
icosa/icosi* 20
polygnum and sides) with the sufx gon from the word triaconta 30
from the Greek polygon. This gon in polygon is said to tetraconta 40
word polygnon, have been derived from the Greek word gonu pentaconta 50
which means hexaconta 60
which means knee, the joint in the middle heptaconta 70
many-angled.
part of a humans leg that resembles an angle octaconta 80
enneaconta 90
when bent. hecta/hecto 100
chilia 1000
Now, to nd out how many sides a hexahectaheptacontakai- myria 10,000
googol 10100
octagon has, we need to know the appropriate Greek prexes together
with some rules for their use. *when used to form 21 29.

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 RULES IN FORMING NUMERICAL PREFIXES
For polygons with: Form numerical prex by:
10 sides or less and multiples of 10 simply copy the prexes for the units digit
11 19 sides* combine: units digit + kai **+ deca
21 99 combining:
tens digit and units digit
multiples of 10 from kai units digit from the
the table table

101 999 combining:

hundreds digit tens digit and units digit

units digit multiples of kai units digit

from the table 10 from the from the table
+ hecta table

* the word kai is often omitted for these numbers (see table for 11 19 at the right)
** the word kai is a Greek word that stands for and and is used before the prex for the units digit

In Euclidean Geometry, the least number of sides for Challenge!

polygons is three. Thus, from the rules and prexes above, we Name the following polygons:
form the polygon with the least number of sides by combining (a) 26-sided polygon
tri and gon to have trigon. This polygon is what we commonly (b) 45-sided polygon
know as the triangle. The tetragon or the four-sided polygon is (c) 102-sided polygon
what we familiarly call quadrilateral. (d) 400-sided polygon
(e) 678-sided polygon
To construct the names of the polygons in the exercises, it
would be helpful to write the number of sides in expanded form
and then nd the equivalent prexes for each number.

a. 26-sided = 20 and (+) 6

icosi kai hexa gon
= icosikaihexagon (sometimes named icosihexagon)
b. 45-sided = 40 + 5
tetraconta kai penta gon
= tetracontakaipentagon (sometimes tetracontapentagon)
c. 102-sided = 100 + 0 + 2
hecta kai di gon
= hectakaidigon
d. 400-sided = 400 + 0 + 0
tetrahecta gon
= tetrahectagon
e. 678-sided = 600 + 70 + 8
hexahecta heptaconta kai octa gon
= hexahectaheptacontakaioctagon

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 So how many sides does a hexahectaheptacontakaioctagon have? Doing the same procedure,
we see that it has 678 sides.

Take note that when you see the word hecta in a name, that means you are in the hundreds place,
conta in the tens (30 - 90) place, and the kai in the ones place. However, sometimes the word kai
is already omitted, just like in the names of polygons with 11 to 19 sides. For instance, to tell how
many sides a heptahectaheptacontaheptagon has, we need to work backwardhepta before gon
means 7, heptaconta means 70, and heptahecta means 700. Thus, the polygon has 777 sides.

Wow! What a name! Did the process confuse you? You probably just need practice in applying
the rules. But dont worry, because as long as you understand what you are referring to when you say
the name, that is all that matters. These days, professional mathematicians consider even prexing
the word gon with the number of sides (n-gons) for polygons beyond enneagons and decagons.

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MORE OR LESS?
Matt and Geo is playing the more or less game but this time with the number of sides of polygons.
Each of them writes ve polygons on a piece of paper. Your task now is to decide who wins between
the two Matt and Geo.

Matts List Geos List

1. icosikaienneagon 1. tetracontakaidigon
2. pentakaidecagon 2. pentadecagon
3. hectaenneacontakaitrigon 3. dihectagon
4. octahectapentacontahenagon 4. heptahectahexacontakaidigon
5. tetrahectohexagon 5. pentahectopentacontagon

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WORKSHEET
A. Connect the polygons from the least to the greatest number of sides then back to the least. What
kind of polygon is inscribed?

B. Name the following polygons.

1. 111-sided
2. 222-sided
3. 333-sided
4. 444-sided
5. 555-sided
6. 666-sided
7. 777-sided
8. 888-sided
9. 999-sided
10. 10 100-sided

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Answer to Activity

Matts list Geos list

icosikaienneagon (29) < tetracontakaidigon (42)
pentakaidecagon (15) = pentadecagon (15)
hectaenneacontakaitrigon (193) < dihectagon (200)
octahectapentacontahenagon (851) > heptahectahexacontakaidigon (762)
tetrahectohexagon (406) < pentahectopentacontagon (550)

Geo wins!

Answer to Worksheet
A. The inscribed polygon is 18-sided or octadecagon.

B.
1. hectahendecagon
2. dihectaicosikaidigon
3. trihectatricontakaitrigon
4. tetrahectatetracontakaitrigon
5. pentahectapentacontakaipentagon or pentahectapentacontapentagon
6. hexahectahexacontakaihexagon or hexahectahexacontahexagon
7. heptahectaheptacontakaiheptagon or heptahectaheptacontaheptagon
8. octahectaoctacontakaioctagon or octahectaoctacontaoctagon
9. enneahectaenneacontakaienneagon or enneahectaenneacontaenneagon
10. googolgon

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