In geometry, the gyroelongated pyramids (also called augmented antiprisms) are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal antiprism.
Gyroelongated pyramid | |
---|---|
Faces | 3n triangles 1 n-gon |
Edges | 5n |
Vertices | 2n + 1 |
Symmetry group | Cnv, [n], (*nn) |
Rotation group | Cn, [n]+, (nn) |
Properties | convex |
There are two gyroelongated pyramids that are Johnson solids made from regular triangles and square, and pentagons. A triangular and hexagonal form can be constructed with coplanar faces. Others can be constructed allowing for isosceles triangles.
Image | Name | Faces |
---|---|---|
Gyroelongated triangular pyramid (Coplanar faces) |
9+1 triangles | |
Gyroelongated square pyramid (J10) | 12 triangles, 1 squares | |
Gyroelongated pentagonal pyramid (J11) | 15 triangles, 1 pentagon | |
Gyroelongated hexagonal pyramid (Coplanar faces) |
18 triangles, 1 hexagon |