# Pentagonal bipyramid

Pentagonal bipyramid
Type Bipyramid
and
Johnson
J12 - J13 - J14
Schläfli symbol { } + {5}
Coxeter diagram
Faces 10 triangles
Edges 15
Vertices 7
Face configuration V4.4.5
Symmetry group D5h, [5,2], (*225), order 20
Rotation group D5, [5,2]+, (225), order 10
Dual pentagonal prism
Properties convex, face-transitive, (deltahedron)

In geometry, the pentagonal bipyramid (or dipyramid) is third of the infinite set of face-transitive bipyramids. Each bipyramid is the dual of a uniform prism.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

If the faces are equilateral triangles, it is a deltahedron and a Johnson solid (J13). It can be seen as two pentagonal pyramids (J2) connected by their bases.

Although it is face-transitive, it is not a Platonic solid because some vertices have four faces meeting and others have five faces.

The pentagonal dipyramid is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size. The other three polyhedra with this property are the regular octahedron, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces.[2]

## Images

It can be drawn as a tiling on a sphere:

## Related polyhedra

The pentagonal bipyramid, dt{2,5}, can be in sequence rectified, rdt{2,5}, truncated, trdt{2,5} and alternated (snubbed), srdt{2,5}:

The dual of the Johnson solid pentagonal bipyramid is the pentagonal prism, with 7 faces: 5 rectangular faces and 2 pentagons.

Dual pentagonal bipyramid Net of dual