A Pentagram is a polygram with 5 lines and angles. like all polygrams, it has at least 1 intersecting line. a Regular Pentagram is what most people call a star.
Threedimensional figures
Further information: Uniform polyhedron: Icosahedral symmetry
Several polyhedra incorporate pentagrams:
Higher dimensions
Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:
4D  5D  

The regular 5cell (4simplex) has 5 vertices and 10 edges.  The rectified 5cell has 10 vertices and 30 edges.  The rectified 5simplex has 15 vertices, seen in this orthogonal projection as 3 nested pentagrams.  The birectified 5simplex has 20 vertices, seen in this orthogonal projection as 4 overlapping pentagrams. 
All ten 4dimensional SchläfliHess polychoron have either pentagrammic faces or vertex figure elements.

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