Hexagonal bipyramid

Hexagonal bipyramid
Type	bipyramid
Faces	12 triangles
Edges	18
Vertices	8
Schläfli symbol	{ } + {6}
Coxeter diagram
Symmetry group	D6h, [6,2], (*226), order 24
Rotation group	D6, [6,2]+, (226), order 12
Dual polyhedron	hexagonal prism
Face configuration	V4.4.6
Properties	convex, face-transitive

A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices and 18 edges. The 12 faces are identical isosceles triangles.

Although it is face-transitive, it is not a Platonic solid because some vertices have four faces meeting and others have six faces, and because its faces cannot be equilateral triangles.

It is one of an infinite set of bipyramids. Having twelve faces, it is a type of dodecahedron, although that name is usually associated with the regular polyhedral form with pentagonal faces. The term dodecadeltahedron is sometimes used to distinguish the bipyramid from the Platonic solid, although in chemistry this term more often refers to the snub disphenoid.

The hexagonal bipyramid has a plane of symmetry (which is horizontal in the figure to the right) where the bases of the two pyramids are joined. This plane is a regular hexagon. There are also six planes of symmetry crossing through the two apices. These planes are rhombic and lie at 30° angles to each other, perpendicular to the horizontal plane.

It can be drawn as a tiling on a sphere which also represents the fundamental domains of [3,2], *322 dihedral symmetry:

The hexagonal bipyramid, dt{2,6}, can be in sequence truncated, tdt{2,6} and alternated (snubbed), sdt{2,6}:

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