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In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
| Uniform pentagrammic antiprism | |
|---|---|
 | |
| Type | Prismatic uniform polyhedron |
| Elements | F = 12, E = 20 V = 10 (χ = 2) |
| Faces by sides | 10{3}+2{5/2} |
| Schläfli symbol | sr{2,5/2} |
| Wythoff symbol | | 2 2 5/2 |
| Coxeter diagram |      |
| Symmetry | D5h, [5,2], (*552), order 20 |
| Rotation group | D5, [5,2]+, (55), order 10 |
| Index references | U79(a) |
| Dual | Pentagrammic trapezohedron |
| Properties | nonconvex |
 Vertex figure 3.3.3.5/2 | |
It has 12 faces, 20 edges and 10 vertices. This polyhedron is identified with the indexed name U79 as a uniform polyhedron.[1]
Note that the pentagram face has an ambiguous interior because it is self-intersecting. The central pentagon region can be considered interior or exterior depending on how interior is defined. One definition of interior is the set of points that have a ray that crosses the boundary an odd number of times to escape the perimeter.
In either case, it is best to show the pentagram boundary line to distinguish it from a concave decagon.
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 An alternative representation with hollow centers to the pentagrams. |
 The pentagrammic trapezohedron is the dual to the pentagrammic antiprism. |
Net (fold the dotted line in the centre in the opposite direction to all the other lines):
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