<s>
A	O
ternary	B-Application
plot	I-Application
,	O
ternary	O
graph	O
,	O
triangle	B-Application
plot	I-Application
,	O
simplex	B-Application
plot	I-Application
,	O
Gibbs	O
triangle	O
or	O
de	O
Finetti	O
diagram	O
is	O
a	O
barycentric	O
plot	B-Application
on	O
three	O
variables	O
which	O
sum	O
to	O
a	O
constant	O
.	O
</s>
<s>
In	O
population	O
genetics	O
,	O
a	O
triangle	B-Application
plot	I-Application
of	O
genotype	O
frequencies	O
is	O
called	O
a	O
de	O
Finetti	O
diagram	O
.	O
</s>
<s>
In	O
game	O
theory	O
,	O
it	O
is	O
often	O
called	O
a	O
simplex	B-Application
plot	I-Application
.	O
</s>
<s>
Ternary	B-Application
plots	I-Application
are	O
tools	O
for	O
analyzing	O
compositional	O
data	O
in	O
the	O
three-dimensional	O
case	O
.	O
</s>
<s>
In	O
a	O
ternary	B-Application
plot	I-Application
,	O
the	O
values	O
of	O
the	O
three	O
variables	O
,	O
,	O
and	O
must	O
sum	O
to	O
some	O
constant	O
,	O
.	O
</s>
<s>
The	O
advantage	O
of	O
using	O
a	O
ternary	B-Application
plot	I-Application
for	O
depicting	O
chemical	O
compositions	O
is	O
that	O
three	O
variables	O
can	O
be	O
conveniently	O
plotted	O
in	O
a	O
two-dimensional	O
graph	O
.	O
</s>
<s>
Ternary	B-Application
plots	I-Application
can	O
also	O
be	O
used	O
to	O
create	O
phase	B-Application
diagrams	I-Application
by	O
outlining	O
the	O
composition	O
regions	O
on	O
the	O
plot	B-Application
where	O
different	O
phases	O
exist	O
.	O
</s>
<s>
The	O
values	O
of	O
a	O
point	O
on	O
a	O
ternary	B-Application
plot	I-Application
correspond	O
(	O
up	O
to	O
a	O
constant	O
)	O
to	O
its	O
trilinear	O
coordinates	O
or	O
barycentric	O
coordinates	O
.	O
</s>
<s>
There	O
are	O
three	O
equivalent	O
methods	O
that	O
can	O
be	O
used	O
to	O
determine	O
the	O
values	O
of	O
a	O
point	O
on	O
the	O
plot	B-Application
:	O
</s>
<s>
Consider	O
an	O
equilateral	O
ternary	B-Application
plot	I-Application
where	O
is	O
placed	O
at	O
and	O
at	O
.	O
</s>
<s>
|Sample	O
3||10%||30%||60%||align	O
=	O
"	O
left	O
"	O
|This	O
sample	O
has	O
the	O
same	O
proportion	O
of	O
clay	O
as	O
Sample	O
2	O
,	O
but	O
the	O
proportions	O
of	O
silt	O
and	O
sand	O
are	O
swapped	O
;	O
the	O
plot	B-Application
is	O
reflected	O
about	O
its	O
vertical	O
axis	O
.	O
</s>
