In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.

It is a special case of a right prism with a pentagram as base, which in general has rectangular non-base faces.

[1] The pentagram face has an ambiguous interior because it is self-intersecting.

One definition of the interior is the set of points from which a ray crosses the boundary an odd number of times; this makes the central pentagon exterior, as every ray beginning within it crosses two edges.

In geometry, the pentagrammic dipyramid (or bipyramid) is first of the infinite set of face-transitive star dipyramids containing star polygon arrangement of edges.