Set of gyroelongated dipyramids | |
---|---|
Faces | 4n triangles |
Edges | 6n |
Vertices | 2n+2 |
Symmetry group | D_{nd} |
Dual polyhedron | truncated trapezohedra |
Properties | convex |
In geometry, the gyroelongated dipyramids or 2n-gonal Deltahedron are an infinite set of polyhedra, constructed by elongating an n-agonal bipyramid by inserting an n-agonal antiprism between its congruent halves.
Two members of the set can be deltahedra, that is, constructed entirely of equilateral triangles: the gyroelongated square dipyramid, a Johnson solid, and the icosahedron, a Platonic solid. The gyroelongated triangular dipyramid can be made with equilateral triangles, but is not a deltahedron because it has coplanar faces, i.e. is not strictly convex. The other members can be constructed with isosceles triangles.
Forms
- Gyroelongated triangular dipyramid - dual triangular truncated trapezohedron
- Gyroelongated square dipyramid - dual square truncated trapezohedron
- Gyroelongated pentagonal dipyramid icosahedron - dual pentagonal truncated trapezohedron dodecahedron
- Gyroelongated hexagonal dipyramid - dual hexagonal truncated trapezohedron
- ...
- n-agonal gyroelongated dipyramid - duals truncated trapezohedron
External links
- Conway Notation for Polyhedra Try: "knAn", where n=4,5,6... example "k5A5" is an icosahedron.
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