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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. 

220px-Star polygon 5-2.svg

Three-dimensional figures

Several polyhedra incorporate pentagrams:

Higher dimensions

Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:

4D 5D
4-simplex t0
The regular 5-cell (4-simplex) has 5 vertices and 10 edges.
4-simplex t1
The rectified 5-cell has 10 vertices and 30 edges.
5-simplex t1 A4
The rectified 5-simplex has 15 vertices, seen in this orthogonal projection as 3 nested pentagrams.
5-simplex t2 A4
The birectified 5-simplex has 20 vertices, seen in this orthogonal projection as 4 overlapping pentagrams.

All ten 4-dimensional Schläfli-Hess polychoron have either pentagrammic faces or vertex figure elements.


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