Gyroelongated bipyramid

Gyroelongated bipyramid
Gyroelongated bipyramid
	The pentagonal gyroelongated bipyramid is the regular icosahedron.
Faces	4n triangles
Edges	6n
Vertices	2n + 2
Symmetry group	Dnd, [2+,2n], (2*n), order 4n
Rotation group	Dn, [2,n]+, (22n), order 2n
Dual polyhedron	truncated trapezohedra
Properties	convex

In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an $n$ -gonal bipyramid by inserting an $n$ -gonal antiprism between its congruent halves.

Gyroelongated bipyramid
The pentagonal gyroelongated bipyramid is the regular icosahedron.
Faces	$4 n$ triangles
Edges	$6 n$
Vertices	$2 n + 2$
Symmetry group	$D n d, [2 +,2 n], (2* n),$ order $4 n$
Rotation group	$D n, [2, n] +, (22 n),$ order $2 n$
Dual polyhedron	truncated trapezohedra
Properties	convex