The word "star" is used in a number of different ways in mathematics. The term is commonly used to voice an asterisk when appearing in a mathematical expression.
For example, 
is voiced "
-star".
The "star" is something used to denote the adjoint 
, or sometimes the complex
conjugate. In common usage, a star is a star polygon
or star figure (i.e., regular convex polygon or polygon
compound) such as the pentagram or hexagram
In plane and solid geometry, a star, sometimes called a sheaf (Ball and Coxeter 1987, p. 141) is defined as a set of 
line segments with a common
midpoint (Coxeter 1973, p. 27). The figures above
show the first few regular 
-stars
in the plane. A star is called nonsingular if no three of the lines comprising it
are coplanar. Every convex
polyhedron bounded by parallelograms determines a nonsingular star, having a
single line segment for each set of 
parallel edges of the polyhedron (Coxeter 1973, p. 27).
In formal geometry, a star is a set of 
vectors 
, ..., 
which form a fixed center in Euclidean 3-space.
In algebraic topology, if 
is a vertex of a simplicial
complex 
,
then the star of 
in 
, denoted 
or 
,
is the union of the interiors of those simplices of 
that have 
as a vertex (Munkres 1993, p. 11).
