Star
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).
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