Elongated triangular dipyramid
Encyclopedia
In geometry
, the elongated triangular bipyramid
(or dipyramid) is one of the Johnson solid
s (J14), convex polyhedra whose faces are regular polygon
s. As the name suggests, it can be constructed by elongating a triangular bipyramid (J12) by inserting a triangular prism
between its congruent halves.
The nirrosula, an African musical instrument woven out of strips of plant leaves, is made in the form of a series of elongated bipyramids with non-equilateral triangles as the faces of their end caps.
e for volume
and surface area
can be used if all faces
are regular
, with edge length a:
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 triangular 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...
(or dipyramid) is one of the 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 (J14), convex polyhedra whose faces are regular polygon
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
s. As the name suggests, it can be constructed by elongating a triangular bipyramid (J12) by inserting a triangular prism
Triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides....
between its congruent halves.
The nirrosula, an African musical instrument woven out of strips of plant leaves, is made in the form of a series of elongated bipyramids with non-equilateral triangles as the faces of their end caps.
Formulae
The following formulaFormula
In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....
e for volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
and surface area
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...
can be used if all faces
Face (geometry)
In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
are regular
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
, with edge length a:
Dual polyhedron
The dual of the elongated triangular bipyramid has 8 faces: 6 trapezoidal and 2 triangular.| Dual elongated triangular bipyramid | Net of dual |
|---|---|