A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point 
in a spherical triangle can be selected so as to trace the
vertices of regular polygonal faces. For example, the Wythoff symbol for the tetrahedron
is 
. There are four types of Wythoff
symbols, 
,
, 
and 
, and one exceptional symbol, 
(which is used for the great
dirhombicosidodecahedron).
The meaning of the bars 
may be summarized as follows (Wenninger 1989, p. 10; Messer 2002). Consider
a spherical triangle 
whose angles are 
, 
, and 
.
1. 
:
is a special point within 
that traces snub polyhedra by even reflections.
2. 
(or 
):
is the vertex 
.
3. 
(or 
):
lies on the arc 
and the bisector of the opposite angle 
.
4. 
(or any permutation of the three letters): 
is the incenter of the triangle 
.
Some special cases in terms of Schläfli symbols are
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
Varying the order of the numbers within a subset of 
, 
,
does not affect the kind of uniform polyhedron.
However, excluding such redundancies, the other permutations of Wythoff symbols using
"
"
and the set of nine rational numbers do not always produce new or valid polyhedra
as some are degenerate forms (Messer 2002).
