The pentagrammic dipyramid is the dual polyhedron of the pentagrammic prism 
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Pentagrammic Dipyramid
See also
Dual Polyhedron, Pentagrammic Prism, Uniform PolyhedronExplore with Wolfram|Alpha
References
Har'El, Z. "Uniform Solution for Uniform Polyhedra." Geom. Dedicata 47, 57-110, 1993. https://doi.org/10.1007/BF01263494.Referenced on Wolfram|Alpha
Pentagrammic DipyramidCite this as:
Weisstein, Eric W. "Pentagrammic Dipyramid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PentagrammicDipyramid.html