Elongated hexagonal bipyramid

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Elongated hexagonal bipyramid
Elongated hexagonal dipyramid.png
Type Elongated dipyramid
Faces 12 triangles
6 squares
Edges 30
Vertices 14
Vertex configuration 2 of 36
12 of 32.42
Symmetry group D6h, [6,2], (*226)
Dual polyhedron Hexagonal bifrustum
Properties convex

In geometry, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid (by inserting a hexagonal prism between its congruent halves).

Related polyhedra[edit]

This polyhedron is in the family of elongated bipyramids, of which the first three can be Johnson solids: J14, J15 and J16. The hexagonal form can be constructed by all regular faces, but isn't a Johnson solid because 6 equilateral triangles would form six co-planar faces (in a regular hexagon).

Uses[edit]

  • A quartz crystal is an example of an elongated hexagonal bipyramid. Because it has 18 faces, it can be called an octadecahedron.
  • The edge-first orthogonal projection of a 24-cell is an elongated hexagonal bipyramid.
  • Used as the outer structure of gelatin-based juice-delivery systems.
  • Used a physical manifestation for assisting various branches of three-dimensional graph theory