Gyroelongated pyramid

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.

Set of gyroelongated pyramids

Example pentagonal form
Faces3n triangles
1 n-gon
Symmetry groupCnv, [n], (*nn)
Rotational groupCn, [n]+, (nn)
Dual polyhedron?

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.


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


  • Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
  • Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.
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