In geometry, the gyroelongated pyramids (also called augmented antiprisms) are an infinite set of polyhedra, constructed by adjoining an pyramid to an antiprism.
There are two gyroelongated pyramids that are Johnson solids made from regular triangles, square, and pentagons. A triangular and hexagonal form can be constructed with coplanar faces. Others can be constructed allowing for isosceles triangles.
Forms 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
See also Gyroelongated bipyramid Elongated bipyramid Elongated pyramid Diminished trapezohedron
References
Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others. The first proof that there are only 92 Johnson solids.