# Elongated triangular cupola

Elongated triangular cupola
Type Johnson
J17 - J18 - J19
Faces 1+3 triangles
3.3 squares
1 hexagon
Edges 27
Vertices 15
Vertex configuration 6(42.6)
3(3.4.3.4)
6(3.43)
Symmetry group C3v
Dual polyhedron -
Properties convex
Net

In geometry, the elongated triangular cupola is one of the Johnson solids (J18). As the name suggests, it can be constructed by elongating a triangular cupola (J3) by attaching a hexagonal prism to its base.

A Johnson solid is one of 92 strictly convex regular-faced polyhedra, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. They are named by Norman Johnson who first enumerated the set in 1966.

## Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]

$V=(\frac{1}{6}(5\sqrt{2}+9\sqrt{3}))a^3\approx3.77659...a^3$

$A=(9+\frac{5\sqrt{3}}{2})a^2\approx13.3301...a^2$

### Dual polyhedron

The dual of the elongated triangular cupola has 15 faces: 6 isosceles triangles, 3 rhombi, and 6 quadrilaterals.

Dual elongated triangular cupola Net of dual

## References

1. ^ Stephen Wolfram, "Elongated triangular cupola" from Wolfram Alpha. Retrieved July 22, 2010.