In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the elongated pentagonal bipyramid or pentakis pentagonal prism is one of the
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johns ...
s (). As the name suggests, it can be constructed by elongating a
pentagonal bipyramid
In geometry, the pentagonal bipyramid (or dipyramid) is third of the infinite set of face-transitive bipyramids, and the 13th Johnson solid (). Each bipyramid is the dual of a uniform prism.
Although it is face-transitive, it is not a Platoni ...
() by inserting a
pentagonal prism
In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices. As a semiregular (or uniform) polyhedron
If faces are all regular, the pentagonal prism is a ...
between its
congruent halves.
Dual polyhedron
The dual of the elongated square bipyramid is a
pentagonal bifrustum
The pentagonal bifrustum or truncated pentagonal bipyramid is the third in an infinite series of bifrustum polyhedra. It has 10 trapezoid and 2 pentagonal faces.
Constructions
The pentagonal bifrustum is the dual polyhedron of a Johnson solid, the ...
.
See also
*
Elongated pentagonal pyramid
In geometry, the elongated pentagonal pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal pyramid () by attaching a pentagonal prism to its base.
Formulae
The following formulae f ...
External links
*
Johnson solids
Pyramids and bipyramids
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