Gyroelongated cupola

Set of gyroelongated cupolae

Example pentagonal form
Faces3n triangles
n squares
1 n-gon
1 2n-gon
Edges9n
Vertices5n
Symmetry groupCnv, [n], (*nn)
Rotational groupCn, [n]+, (nn)
Dual polyhedron
Propertiesconvex

In geometry, the gyroelongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an n-gonal antiprism.

There are three gyroelongated cupolae that are Johnson solids made from regular triangles and square, and pentagons. Higher forms can be constructed with isosceles triangles. Adjoining a triangular prism to a square antiprism also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid. The hexagonal form can be constructed from regular polygons, but the cupola faces are all in the same plane. Topologically other forms can be constructed without regular faces.

Forms

name faces
gyroelongated triangular prism 2+8 triangles, 2+1 square
gyroelongated triangular cupola (J22) 9+1 triangles, 3 squares, 1 hexagon
gyroelongated square cupola (J23) 12 triangles, 4+1 squares, 1 octagon
gyroelongated pentagonal cupola (J24) 15 triangles, 5 squares, 1 pentagon, 1 decagon
gyroelongated hexagonal cupola 18 triangles, 6 squares, 1 hexagon, 1 dodecagon

See also

References


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