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 | |
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Type | Star bipyramid |
Faces | 10 triangles |
Edges | 15 |
Vertices | 7 |
Schläfli symbol | {} + {5/2} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | D5h, [5,2], (*225), order 20 |
Rotation group | D5, [5,2]+, (225), order 10 |
Dual polyhedron | pentagrammic prism |
Face configuration | V4.4.5 |
Properties | face-transitive, (deltahedron) |
![](../I/m/Pentagrammic_bipyramid_(dual_uniform).stl.png)
3D model of a dual uniform pentagrammic bipyramid
![](../I/m/Pentagrammic_bipyramid_(regular_faces).stl.png)
3D model of a pentagrammic bipyramid with regular faces
Each star bipyramid is the dual of a star polygon based uniform prism.
Related polyhedra
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 |
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References
External links
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