Elongated bipyramid
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid (by inserting an n-gonal prism between its congruent halves).
| Elongated bipyramid | |
|---|---|
 Example: elongated hexagonal bipyramid | |
| Faces | 2n triangles n squares |
| Edges | 5n |
| Vertices | 2n + 2 |
| Symmetry group | Dnh, [n,2], (*n22) |
| Rotation group | Dn, [n,2]+, (n22) |
| Dual polyhedron | bifrustums |
| Properties | convex |
There are three elongated bipyramids that are Johnson solids:
- Elongated triangular bipyramid (J14),
- Elongated square bipyramid (J15), and
- Elongated pentagonal bipyramid (J16).
Higher forms can be constructed with isosceles triangles.
Forms
| Name | elongated triangular bipyramid J14 |
elongated square bipyramid J15 |
elongated pentagonal bipyramid J16 |
elongated hexagonal bipyramid |
|---|---|---|---|---|
| Type | Equilateral | Irregular | ||
| Image |  |
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| Faces | 6 triangles, 3 squares |
8 triangles, 4 squares |
10 triangles, 5 squares |
12 triangles, 6 squares |
| Dual | triangular bifrustum | square bifrustum | pentagonal bifrustum | hexagonal bifrustum |
References
- Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
- Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.
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