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.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

Formulae

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

${\displaystyle V=({\frac {1}{6))(5{\sqrt {2))+9{\sqrt {3))))a^{3}\approx 3.77659...a^{3))$

${\displaystyle A=(9+{\frac {5{\sqrt {3))}{2)))a^{2}\approx 13.3301...a^{2))$

Dual polyhedron

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

Dual elongated triangular cupola	Net of dual