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### Naming Polygons

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Date: 30 May 1995 10:09:38 -0400
From: Trevor Ratcliff
Newsgroups: local.dr-math
Subject: Naming Polygons

Dr. Math:

Could you please give me a complete list of polygon names, from 3 - 100,
if such a list exists?

Thanks Martial and Ratman
```

```
Date: 30 May 1995 22:52:57 -0400
From: Sarah Seastone
Subject: Materials for Naming Polygons

For a full list of polygon names, see "Names of polygons and polyhedra" in the Dr. Math FAQ:

http://mathforum.org/dr.math/faq/faq.polygon.names.html

Following are some of the contributions that were made by Prof. John
Conway to the newsgroup geometry.pre-college on the subject of naming
polygons.  The full discussions are archived at

http://mathforum.org/kb/message.jspa?messageID=1076464&tstart=0

_____________________________________________________________

From: "John Conway"
Subject:    Re: 11-gon
Date:       Mon, 24 Oct 94 20:10:39 EDT

I have obviously missed an interesting discussion on names for polygons!

Anyway, I'll throw in what I know, since such things have always interested me.

1) For the "numerical" part of the name, one should use the Greek
prefixes:

mono, di, tri, tetra, penta, hexa, hepta, octa, ennea,

deca, hendeca, dodeca, trideca, etc, icosa, triaconta, hecta ..

10      11      12      13            20       30      100

A 24-gon would thus officially be an icositetragon.

There are variations in spelling and formation

(eg   dekagon, endecagon, triskaidecagon,...)

(the "kai" here means "and")

The "gon" has an interesting etymology : it is ultimately
derived from the Greek word "gonu" for "knee", which they
transferred to "angle".

This word goes straight back to the Indo-European, and is
essentially the same in lots of languages:

gonu    (greek)
genu    (latin)
k nee   (english)

French is similar to Latin here, and German to English  (except
that the "K" is still pronounced.

3)  The "hedron" in "polyhedron" is also an Indo-European
word, meaning "seat".  A "cathedral" church is one that contains
a seat from which a bishop hands down authoritative opinions
(cata = down,  hedron = seat).

In accordance with Grimm's law, the "h" is  Greek
corresponds to "s" in English, while "d" may soften to "t"
and "p" or "b" to  "f" or "v".  So look:

penta
five       hexa
six       hepta
seven      hedr
seat    ped
foot

4)  In summary, a "polygon" is a thing with many knees,
and a "polyhedron" a thing with many seats.

I mentioned "ped" because it happens in that curious
word "parallelepiped", which should really be pronounced
parallel-epi-ped.  Until about the middle of the 19th century
this word was even longer - "parallelepipedon".  It splits
into parts thus

para - allele - epi - ped - on

beside   other  upon    ground

(memo - "pedon", meaning the ground, is what you put your foot on)

Two things are "parallel" if one is beside the other - this was
already used as a single word very early on.  What the name
means is that there's always a face that's parallel to the one
upon the ground.

The term "allele" in modern biological use, is one of the
"alternatives" that goes in a certain place along a chromosome.

5)  The word "trapezium" has an interesting history.  A
Greek word for "table" was  "tetrapedon" or "tetrapes", meaning
"four legs".  This then was used for "table-shaped", meaning
around a bit over the years.  Originally, it was used only for
rectangles, but later for arbitrary quadrilaterals, and it is only
quite recently that is has been specialized to those with two
parallel sides.  So in some scientific uses, "trapezoidal"
refers to things with arbitrary quadrilateral faces, not just
to those whose faces are trapeziums in the modern sense.

By the way, of course the circus "trapeze" is just a
trapezium, in the sense of "rectangle".

I hope that someone else out there finds this nearly as
interesting as I do.

John Conway
______________________________________________

From: "John Conway"
Subject:    Re: 11-gon
Date:       Mon, 24 Oct 94 21:16:16 EDT

"official" names are

icositetragon

tetracontaoctagon

enneacontahexagon

if anyone cares.   A "myriagon" would be a polygon with 10000 sides.

The word "macaronic" is usually used for a word made of pieces
from several languages - one doesn't need "linguistic heteromorph"!

John Conway
______________________________________________

From: "John Conway"
Subject:    Re: 11-gon
Date:       Mon, 24 Oct 94 21:21:28 EDT

By the way, "icositetrahedron" appears in some dictionaries.

The dual of the rhombicuboctahedron has been called either
a trapezoidal or tetragonal icositetrahedron, while the dual
of the snub cube is a pentagonal icositetrahedron.

I saw the word "tetrakaidecahedron" in a recent "press release"
from the Minneapolis Geometry Center, so you can see that people
DO occasionally use such words.

John Conway
______________________________________________

From: "John Conway"
Subject:    Re: 11-gon
Date:       Mon, 24 Oct 94 21:35:08 EDT

I'm working my way back through all this email.  I see that
"undecagon" and "duodecagon" have been rearing their ugly
heads again.  The full set is

monogon, digon, trigon, tetragon, pentagon, hexagon, heptagon, octagon

(of which monogon and digon can only be used in rather special circumstances;

it's digon not "bigon"; and trigon and tetragon are alternatives to "triangle"
being more common), then

enneagon, decagon, hendecagon, dodecagon, triskaidecagon, tetrakaidecagon,...

not

nonagon            undecagon   duodecagon

are OK.

The (synonymous) words "triskaidecaphobia" and "tridecaphobia"
appear in dictionaries (occasionally spelled with a "k" instead
of that "c").  I was reminded of them in O'Hare airport yesterday,
as I passed gates 10,11,12,14,15,...  !

John Conway

```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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