Elongated dipyramid
Encyclopedia
| Set of elongated dipyramids | |
|---|---|
 |
|
| Faces | 2n triangle Triangle A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted .... s, n square Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... s |
| Edges | 5n |
| Vertices | 2n+2 |
| Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation... |
Dnh |
| Dual polyhedron Dual polyhedron In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another... |
bifrustum Bifrustum An n-agonal bifrustum is a polyhedron composed of three parallel planes of n-agons, with the middle plane largest and usually the top and bottom congruent.... s |
| Properties | convex |
In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid
Bipyramid
An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.The referenced n-gon in the name of the bipyramids is not an external face but an internal one, existing on the primary symmetry plane which connects the two pyramid halves.The...
(by inserting an n-gonal prism
Prism (geometry)
In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...
between its congruent halves).
There are three elongated bipyramids that are Johnson solid
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s made from regular triangles and squares. Higher forms can be constructed with isosceles triangles.
Forms
| name | faces | dual | |
|---|---|---|---|
 |
elongated triangular bipyramid (J14) | 6 triangles, 3 squares | triangular bifrustum Triangular bifrustum The triangular bifrustum or triangular truncated bipyramid is the second in an infinite series of bifrustum polyhedra. It has 6 trapezoid and 2 triangle faces.... |
 |
elongated square bipyramid (J15) | 8 triangles, 4 squares | square bifrustum Square bifrustum The square bifrustum or square truncated bipyramid is the second in an infinite series of bifrustum polyhedra. It has 4 trapezoid and 2 square faces.... |
 |
elongated pentagonal bipyramid (J16) | 10 triangles, 5 squares | pentagonal bifrustum Pentagonal bifrustum The pentagonal bifrustum or pentagonal truncated bipyramid is the third in an infinite series of bifrustum polyhedra. It has 10 trapezoid and 2 pentagonal faces. It is the dual of the Johnson solid, elongated pentagonal dipyramid.... |
| |
elongated hexagonal bipyramid | 12 triangles, 6 squares | hexagonal bifrustum Hexagonal bifrustum The hexagonal bifrustum or truncated bipyramid is the fourth in an infinite series of bifrustum polyhedra. It has 12 trapezoid and 2 hexagonal faces.... |
| n-gonal elongated bipyramid | 2n triangles, n squares | bifrustum Bifrustum An n-agonal bifrustum is a polyhedron composed of three parallel planes of n-agons, with the middle plane largest and usually the top and bottom congruent.... |