Pentagrammic bipyramid

In geometry, the pentagrammic bipyramid (or dipyramid) is first of the infinite set of face-transitive star bipyramids containing star polygon arrangement of edges. It has 10 intersecting isosceles triangle faces. It is topologically identical to the pentagonal bipyramid.

Pentagrammic bipyramid
TypeStar bipyramid
Faces10 triangles
Edges15
Vertices7
Schläfli symbol{} + {5/2}
Coxeter diagram
Symmetry groupD5h, [5,2], (*225), order 20
Rotation groupD5, [5,2]+, (225), order 10
Dual polyhedronpentagrammic prism
Face configurationV4.4.5
Propertiesface-transitive, (deltahedron)
3D model of a dual uniform pentagrammic bipyramid
3D model of a pentagrammic bipyramid with regular faces

Each star bipyramid is the dual of a star polygon based uniform prism.

There are two pentagrammic trapezohedra (or deltohedra), being dual to the pentagrammic antiprism and pentagrammic crossed antiprism respectively, each having intersecting kite-shaped faces (convex or concave), and a total of 12 vertices:

{​5⁄2} trapezohedron {​5⁄3} trapezohedron

References
    • Weisstein, Eric W. "Dipyramid". MathWorld.
    • Weisstein, Eric W. "Pentagrammic dipyramid". MathWorld.
    • Weisstein, Eric W. "Pentagrammic deltohedron". MathWorld.
    • Weisstein, Eric W. "Pentagrammic concave deltohedron". MathWorld.
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